Question 1

Find an equation for the conic whose graph is shown.

Accepted Answer

A)    x2=4(y+3) x ^ { 2 } = 4 ( y + 3 ) x2=4(y+3)  
B)    x2=3(y+3) x ^ { 2 } = 3 ( y + 3 ) x2=3(y+3)  
C)    y2=12(x+3) y ^ { 2 } = 12 ( x + 3 ) y2=12(x+3)  
D)    x12=(y+3) 2\frac { x } { 12 } = ( y + 3 )  ^ { 2 }12x​=(y+3) 2 
E)    x2=12(y+3) x ^ { 2 } = 12 ( y + 3 ) x2=12(y+3) F) B) and C)
G) C) and D)

Question 2

Find the vertices and foci for the ellipse. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$

Accepted Answer

Vertices: ...

Question 3

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

Accepted Answer

The answer of Complete the square to determine the type...

Question 4

Find the eccentricity and identify the conic given by $r = \frac { 2 } { 1 - \cos \theta }$ 
.

Accepted Answer

, so the...

Question 5

Find the lengths of the major and minor axes for the ellipse.  x213+y249=1\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 113x2​+49y2​=1

Accepted Answer

A)   major axis:  141414 , minor:  2132 \sqrt { 13 }213c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)   major axis:  777 , minor:  2142 \sqrt { 14 }214c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)   major axis:  494949 , minor:  2132 \sqrt { 13 }213c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)   major axis:  141414 , minor:  141414 
E)   none of these F) A) and B)
G) A) and C)

Question 6

Find an equation of the parabola whose graph is shown.

Accepted Answer

The answer of Find an equation of the parabola whose...

Question 7

Determine the  XY‾\overline { X Y }XY  - coordinates of  (−2,5) ( - 2,5 ) (−2,5)  
If the axes are rotated through an angle  ϕ=30∘\phi = 30 ^ { \circ }ϕ=30∘

Accepted Answer

A)    X=5−232X = \frac { 5 - 2 \sqrt { 3 } } { 2 }X=25−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=2+532Y = \frac { 2 + 5 \sqrt { 3 } } { 2 }Y=22+53c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    X=232X = \frac { 2 \sqrt { 3 } } { 2 }X=223c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=1−532Y = 1 - \frac { 5 \sqrt { 3 } } { 2 }Y=1−253c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    X=5−23X = 5 - 2 \sqrt { 3 }X=5−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ ,  Y=1+32Y = 1 + \frac { \sqrt { 3 } } { 2 }Y=1+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    X=5−232X = \frac { 5 - 2 \sqrt { 3 } } { 2 }X=25−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=3+52Y = \frac { \sqrt { 3 } + 5 } { 2 }Y=23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+5​ 
E)    X=1+232X = \frac { 1 + 2 \sqrt { 3 } } { 2 }X=21+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=−5+32Y = - 5 + \frac { \sqrt { 3 } } { 2 }Y=−5+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​F) B) and D)
G) D) and E)

Question 8

Determine the  XY‾\overline { X Y }XY  - coordinates of  (−2,5) ( - 2,5 ) (−2,5)   If the axes are rotated through an angle  ϕ=30∘\phi = 30 ^ { \circ }ϕ=30∘

Accepted Answer

A)    X=5−232X = \frac { 5 - 2 \sqrt { 3 } } { 2 }X=25−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=2+532Y = \frac { 2 + 5 \sqrt { 3 } } { 2 }Y=22+53c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    X=232X = \frac { 2 \sqrt { 3 } } { 2 }X=223c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=1−532Y = 1 - \frac { 5 \sqrt { 3 } } { 2 }Y=1−253c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    X=5−23X = 5 - 2 \sqrt { 3 }X=5−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ ,  Y=1+32Y = 1 + \frac { \sqrt { 3 } } { 2 }Y=1+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    X=5−232X = \frac { 5 - 2 \sqrt { 3 } } { 2 }X=25−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=3+52Y = \frac { \sqrt { 3 } + 5 } { 2 }Y=23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+5​ 
E)    X=1+232X = \frac { 1 + 2 \sqrt { 3 } } { 2 }X=21+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ ,  Y=−5+32Y = - 5 + \frac { \sqrt { 3 } } { 2 }Y=−5+23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​F) A) and E)
G) C) and E)

Question 9

Sketch the graph of the parabola.  2x+7y2=02 x + 7 y ^ { 2 } = 02x+7y2=0

Accepted Answer

A)  
B)  
C)  
D)   E) A) and D)
F) None of the above

Question 10

Find the vertices and foci for the ellipse.  y2=4−2x2y ^ { 2 } = 4 - 2 x ^ { 2 }y2=4−2x2

Accepted Answer

A)  Vertices:  (0,±2) ( 0 , \pm \sqrt { 2 } ) (0,±2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  , foci:  (0,±2) ( 0 , \pm 2 ) (0,±2)  
B)  Vertices:  (±2,0) ( \pm 2,0 ) (±2,0)  , foci:  (0,±2) ( 0 , \pm \sqrt { 2 } ) (0,±2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
C)  Vertices:  (0,±2) ( 0 , \pm 2 ) (0,±2)  , foci:  (0,±2) ( 0 , \pm \sqrt { 2 } ) (0,±2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  
D)  Vertices:  (0,±2) ( 0 , \pm 2 ) (0,±2)  , foci:  (±2,0) ( \pm \sqrt { 2 } , 0 ) (±2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,0)  
E)   none of these F) All of the above
G) A) and B)

Question 11

Find an equation of the parabola whose graph is shown.

Accepted Answer

A)    x2=4yx ^ { 2 } = 4 yx2=4y 
B)    x2=16yx ^ { 2 } = 16 yx2=16y 
C)    y2=16xy ^ { 2 } = 16 xy2=16x 
D)    y2=8xy ^ { 2 } = 8 xy2=8x 
E)   none of these F) C) and D)
G) A) and B)

Question 12

A cannon fires a cannonball as shown in the figure. The path of the cannonball is a parabola with vertex at the highest point of the path. If the cannonball lands 800 ft from the cannon and the highest point it reaches is 1600 ft above the ground, find an equation for the path of the cannonball. Place the origin at the location of the cannon.

Accepted Answer

The answer of A cannon fires a cannonball as shown...

Question 13

Find an equation for the conic whose graph is shown.

Accepted Answer

The answer of Find an equation for the conic whose...

Question 14

Sketch the graph of the parabola. $$2 x + 7 y ^ { 2 } = 0$$

Accepted Answer

The answer of Sketch the graph of the parabola. \[2...

Question 15

Sketch the graph of the parabola. $$y ^ { 2 } + 2 y - 12 x + 37 = 0$$

Accepted Answer

The answer of Sketch the graph of the parabola. \[y...

Question 16

Write a polar equation of an ellipse with eccentricity $0.3$ 
and directrix $y = - 7$ 
.

Accepted Answer

The answer of Write a polar equation of an ellipse...

Question 17

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Accepted Answer

The answer of Complete the square to determine the type...

Question 18

Find an equation for parabola with vertex $( - 1,3 )$ 
and directrix $x = - 4$ 
.

Accepted Answer

The answer of Find an equation for parabola with vertex...

Question 19

Sketch the graph of the ellipse.  (x−5) 236+y29=1\frac { ( x - 5 )  ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 136(x−5) 2​+9y2​=1

Accepted Answer

A)   
B)   
C)  
D)  
E)  none of these F) A) and B)
G) A) and C)

Question 20

Sketch the graph of the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

Accepted Answer

, Center:

, foci...

Exam 12: Conic Sections

Find the eccentricity and identify the conic given by $r = \frac { 2 } { 1 - \cos \theta }$ .

Correct Answer
verified

, so the...
View Answer

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Correct Answer
verified

Sketch the graph of the parabola. $2 x + 7 y ^ { 2 } = 0$

Correct Answer
verified

Determine the $\overline { X Y }$ - coordinates of $( - 2,5 )$ If the axes are rotated through an angle $\phi = 30 ^ { \circ }$

Correct Answer
verified

Find the lengths of the major and minor axes for the ellipse. $\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 1$

Correct Answer
verified

Find the vertices and foci for the ellipse. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$

Correct Answer
verified
Vertices: ...
View Answer

Find an equation of the parabola whose graph is shown.

Correct Answer
verified

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Correct Answer
verified

Find an equation of the parabola whose graph is shown. $Find an equation of the parabola whose graph is shown. A) x ^ { 2 } = 4 y B) x ^ { 2 } = 16 y C) y ^ { 2 } = 16 x D) y ^ { 2 } = 8 x E) none of these$

Correct Answer
verified

Sketch the graph of the parabola. $2 x + 7 y ^ { 2 } = 0$

Correct Answer
verified

Determine the $\overline { X Y }$ - coordinates of $( - 2,5 )$ If the axes are rotated through an angle $\phi = 30 ^ { \circ }$

Correct Answer
verified

Find an equation for parabola with vertex $( - 1,3 )$ and directrix $x = - 4$ .

Correct Answer
verified

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$ .

Correct Answer
verified

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

Correct Answer
verified

Find an equation for the conic whose graph is shown. $Find an equation for the conic whose graph is shown. A) x ^ { 2 } = 4 ( y + 3 ) B) x ^ { 2 } = 3 ( y + 3 ) C) y ^ { 2 } = 12 ( x + 3 ) D) \frac { x } { 12 } = ( y + 3 ) ^ { 2 } E) x ^ { 2 } = 12 ( y + 3 )$

Correct Answer
verified

Find an equation for the conic whose graph is shown.

Correct Answer
verified

Sketch the graph of the ellipse. $\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$

Correct Answer
verified

Sketch the graph of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Correct Answer
verified

Correct Answer
verified

Sketch the graph of the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

Correct Answer
verified

, Center:
, foci...
View Answer

Exam 12: Conic Sections

Find the eccentricity and identify the conic given by r=21−cos⁡θr = \frac { 2 } { 1 - \cos \theta }r=1−cosθ2​ .

Correct Answerverified , so the...View AnswerShow Answer

Complete the square to determine the type of curve represented by the equation. x2+6x−3y2+12y=12x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12x2+6x−3y2+12y=12

Correct AnswerverifiedShow Answer

Sketch the graph of the parabola. 2x+7y2=02 x + 7 y ^ { 2 } = 02x+7y2=0

Correct AnswerverifiedShow Answer

Determine the XY‾\overline { X Y }XY - coordinates of (−2,5) ( - 2,5 ) (−2,5) If the axes are rotated through an angle ϕ=30∘\phi = 30 ^ { \circ }ϕ=30∘

Correct AnswerverifiedShow Answer

Find the lengths of the major and minor axes for the ellipse. x213+y249=1\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 113x2​+49y2​=1

Correct AnswerverifiedShow Answer

Find the vertices and foci for the ellipse. 4x2+9y2=364 x ^ { 2 } + 9 y ^ { 2 } = 364x2+9y2=36

Correct AnswerverifiedVertices: ...View AnswerShow Answer

Find an equation of the parabola whose graph is shown.

Correct AnswerverifiedShow Answer

Find the vertices and foci for the ellipse. y2=4−2x2y ^ { 2 } = 4 - 2 x ^ { 2 }y2=4−2x2

Correct AnswerverifiedShow Answer

Find an equation of the parabola whose graph is shown.

Correct AnswerverifiedShow Answer

Sketch the graph of the parabola. 2x+7y2=02 x + 7 y ^ { 2 } = 02x+7y2=0

Correct AnswerverifiedShow Answer

Determine the XY‾\overline { X Y }XY - coordinates of (−2,5) ( - 2,5 ) (−2,5) If the axes are rotated through an angle ϕ=30∘\phi = 30 ^ { \circ }ϕ=30∘

Correct AnswerverifiedShow Answer

Find an equation for parabola with vertex (−1,3)( - 1,3 )(−1,3) and directrix x=−4x = - 4x=−4 .

Correct AnswerverifiedShow Answer

Write a polar equation of an ellipse with eccentricity 0.30.30.3 and directrix y=−7y = - 7y=−7 .

Correct AnswerverifiedShow Answer

Complete the square to determine the type of curve represented by the equation. 4x2+9y2−16x−20=04 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 04x2+9y2−16x−20=0

Correct AnswerverifiedShow Answer

Find an equation for the conic whose graph is shown.

Correct AnswerverifiedShow Answer

Find an equation for the conic whose graph is shown.

Correct AnswerverifiedShow Answer

Sketch the graph of the ellipse. (x−5) 236+y29=1\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 136(x−5) 2​+9y2​=1

Correct AnswerverifiedShow Answer

Sketch the graph of the parabola. y2+2y−12x+37=0y ^ { 2 } + 2 y - 12 x + 37 = 0y2+2y−12x+37=0

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Sketch the graph of the hyperbola. y2−2y−4x2−16x=15y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15y2−2y−4x2−16x=15

Correct Answerverified , Center: , foci...View AnswerShow Answer

Find the eccentricity and identify the conic given by $r = \frac { 2 } { 1 - \cos \theta }$ .

Correct Answer
verified

, so the...
View Answer

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Correct Answer
verified

Sketch the graph of the parabola. $2 x + 7 y ^ { 2 } = 0$

Correct Answer
verified

Determine the $\overline { X Y }$ - coordinates of $( - 2,5 )$ If the axes are rotated through an angle $\phi = 30 ^ { \circ }$

Correct Answer
verified

Find the lengths of the major and minor axes for the ellipse. $\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 1$

Correct Answer
verified

Find the vertices and foci for the ellipse. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$

Correct Answer
verified
Vertices: ...
View Answer

Correct Answer
verified

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Correct Answer
verified

Find an equation of the parabola whose graph is shown. $Find an equation of the parabola whose graph is shown. A) x ^ { 2 } = 4 y B) x ^ { 2 } = 16 y C) y ^ { 2 } = 16 x D) y ^ { 2 } = 8 x E) none of these$

Correct Answer
verified

Sketch the graph of the parabola. $2 x + 7 y ^ { 2 } = 0$

Correct Answer
verified

Determine the $\overline { X Y }$ - coordinates of $( - 2,5 )$ If the axes are rotated through an angle $\phi = 30 ^ { \circ }$

Correct Answer
verified

Find an equation for parabola with vertex $( - 1,3 )$ and directrix $x = - 4$ .

Correct Answer
verified

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$ .

Correct Answer
verified

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

Correct Answer
verified

Find an equation for the conic whose graph is shown. $Find an equation for the conic whose graph is shown. A) x ^ { 2 } = 4 ( y + 3 ) B) x ^ { 2 } = 3 ( y + 3 ) C) y ^ { 2 } = 12 ( x + 3 ) D) \frac { x } { 12 } = ( y + 3 ) ^ { 2 } E) x ^ { 2 } = 12 ( y + 3 )$

Correct Answer
verified

Correct Answer
verified

Sketch the graph of the ellipse. $\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$

Correct Answer
verified

Sketch the graph of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Correct Answer
verified

Correct Answer
verified

Sketch the graph of the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

Correct Answer
verified

, Center:
, foci...
View Answer