Question 1

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci: $( 5,3 ) , ( 5,13 )$ ,endpoints of the major axis: $( 5,0 ) , ( 5,16 )$ ​

Accepted Answer

A)  $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 39 } = 1$ 
B)  $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y - 8 ) ^ { 2 } } { 39 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 39 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 39 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$ 
E)  $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 39 } = 1$ 
A)  $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 39 } = 1$ 
B)  $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y - 8 ) ^ { 2 } } { 39 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 39 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 39 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$ 
E)  $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 39 } = 1$ D

Question 2

Find the standard form of the equation of the ellipse with the given characteristics. ​
Center: $( - 6,4 )$ ,a = 5c,foci: $( - 8,4 ) , ( - 4,4 )$ ,where a - thr semimajor axis,b - semiminor axis and $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ .

Accepted Answer

A)  $\frac { ( x - 6 ) ^ { 2 } } { 96 } + \frac { ( y + 4 ) ^ { 2 } } { 100 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 96 } + \frac { ( y - 4 ) ^ { 2 } } { 100 } = 1$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 100 } + \frac { ( y - 4 ) ^ { 2 } } { 96 } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { 100 } + \frac { ( y + 6 ) ^ { 2 } } { 96 } = 1$ 
E)  $\frac { ( x + 4 ) ^ { 2 } } { 100 } + \frac { ( y - 6 ) ^ { 2 } } { 96 } = 1$ 
A)  $\frac { ( x - 6 ) ^ { 2 } } { 96 } + \frac { ( y + 4 ) ^ { 2 } } { 100 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 96 } + \frac { ( y - 4 ) ^ { 2 } } { 100 } = 1$ 
C)  $\frac { ( x + 6 ) ^ { 2 } } { 100 } + \frac { ( y - 4 ) ^ { 2 } } { 96 } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { 100 } + \frac { ( y + 6 ) ^ { 2 } } { 96 } = 1$ 
E)  $\frac { ( x + 4 ) ^ { 2 } } { 100 } + \frac { ( y - 6 ) ^ { 2 } } { 96 } = 1$ C

Question 3

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Foci: $( \pm 5,0 )$ ;major axis of length 12
​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 11 } = 1$ 
B)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 5 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 11 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 11 } = 1$ 
A)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 11 } = 1$ 
B)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 5 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 11 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 11 } = 1$ D

Question 4

Find the standard form of the equation of the ellipse with the following characteristics. ​
Foci: $( \pm 2,0 )$ ,major axis of length: 22
​
​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 117 } = 1$ 
B)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 480 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 121 } = 1$ 
A)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 117 } = 1$ 
B)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 480 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 121 } = 1$

Question 5

Find the center and the vertices of the ellipse.​ $81 x ^ { 2 } + y ^ { 2 } = 81$ ​

Accepted Answer

A) center: (-9,9);vertices: (-1,-9), (1,9) 
B) center: (0,0);vertices: (0,-9), (0,9) 
C) center: (0,0);vertices: (-9,-1), (9,1) 
D) center: (0,0);vertices: (-9,0), (9,0) 
E) center: (-9,9);vertices: (-1,0), (1,0) 
A) center: (-9,9);vertices: (-1,-9), (1,9) 
B) center: (0,0);vertices: (0,-9), (0,9) 
C) center: (0,0);vertices: (-9,-1), (9,1) 
D) center: (0,0);vertices: (-9,0), (9,0) 
E) center: (-9,9);vertices: (-1,0), (1,0)

Question 6

Find the center and radius of the conic.​ $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$ ​

Accepted Answer

A) Center: $( 0,8 )$ Radius: 8 
B) Center: $( 0,0 )$ Radius: 8 
C) Center: (0,0) Radius: $64$ 
D) Center: $( 8,0 )$ Radius: 8 
E) Center: $( 0,8 )$ Radius: $64$ 
A) Center: $( 0,8 )$ Radius: 8 
B) Center: $( 0,0 )$ Radius: 8 
C) Center: (0,0) Radius: $64$ 
D) Center: $( 8,0 )$ Radius: 8 
E) Center: $( 0,8 )$ Radius: $64$

Question 7

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.​   ​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x } { 4 } + \frac { y } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 16 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x } { 4 } + \frac { y } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 8

Select the graph for following equation.​ $$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 9

Select the graph for following equation.​ $$\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 10

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci: $( - 5 , - 12 ) , ( - 5 , - 4 )$ ,endpoints of the major axis: $( - 5 , - 16 ) , ( - 5,0 )$ ​

Accepted Answer

A)  $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y + 8 ) ^ { 2 } } { 48 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 48 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$ 
C)  $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 48 } = 1$ 
D)  $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 48 } = 1$ 
E)  $\frac { ( x + 5 ) ^ { 2 } } { 48 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$ 
A)  $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y + 8 ) ^ { 2 } } { 48 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 48 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$ 
C)  $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 48 } = 1$ 
D)  $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 48 } = 1$ 
E)  $\frac { ( x + 5 ) ^ { 2 } } { 48 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$

Question 11

Find the standard form of the equation of the ellipse with the following characteristics. ​
Foci: $( \pm 3,0 )$ ,major axis of length: 16
​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 55 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$ 
D)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 247 } = 1$ 
A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 55 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$ 
D)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 247 } = 1$

Question 12

Identify the conic as a circle or an ellipse then find the center.​ $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ ​

Accepted Answer

A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) ​Circle Center: (3,2) 
D) ​Ellipse Center: (3,2) 
E) ​Circle Center: (2,3) 
A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) ​Circle Center: (3,2) 
D) ​Ellipse Center: (3,2) 
E) ​Circle Center: (2,3)

Question 13

Write the equation of the ellipse that has its center at the origin,focus at (1,0)and vertex at (9,0). ​

Accepted Answer

A)  $$\frac { x ^ { 2 } } { 80 } + \frac { y ^ { 2 } } { 81 } = 1$$ 
B)  $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = - 1$ 
D)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 80 } = 1$ 
E)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = 1$ 
A)  $$\frac { x ^ { 2 } } { 80 } + \frac { y ^ { 2 } } { 81 } = 1$$ 
B)  $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = - 1$ 
D)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 80 } = 1$ 
E)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = 1$

Question 14

Find the center and foci of the ellipse.​ $$\frac { ( x - 2 ) ^ { 2 } } { 45 } + \frac { ( y - 8 ) ^ { 2 } } { 81 } = 1$$ ​

Accepted Answer

A) center: $( - 2 , - 8 )$ ;foci: $( - 2 , - 14 ) , ( - 2 , - 2 )$ 
B) center: $( 2,8 )$ ;foci: $( 2,2 ) , ( 2,14 )$ 
C) center: $( 2,8 )$ ;foci: $( 14,8 ) , ( 8,8 )$ 
D) center: $( - 2 , - 8 )$ ;foci: $( - 8,8 ) , ( - 14,8 )$ 
E) center: $( 2,8 )$ ;foci: $( - 8 , - 8 ) , ( - 14 , - 8 )$ 
A) center: $( - 2 , - 8 )$ ;foci: $( - 2 , - 14 ) , ( - 2 , - 2 )$ 
B) center: $( 2,8 )$ ;foci: $( 2,2 ) , ( 2,14 )$ 
C) center: $( 2,8 )$ ;foci: $( 14,8 ) , ( 8,8 )$ 
D) center: $( - 2 , - 8 )$ ;foci: $( - 8,8 ) , ( - 14,8 )$ 
E) center: $( 2,8 )$ ;foci: $( - 8 , - 8 ) , ( - 14 , - 8 )$

Question 15

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertices: $( 0 , \pm 8 )$ ;Foci: $( 0 , \pm 4 )$ ​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 48 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 48 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$ 
A)  $\frac { x ^ { 2 } } { 48 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 48 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$

Question 16

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse.​ $\frac { x ^ { 2 } } { 4 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 49 } = 1$ ​

Accepted Answer

A) Ellipse Center: $\frac { 2 } { 7 }$ 
B) Ellipse Center: 1 
C) Circle Radius: 1 
D) Circle Radius: $\frac { 2 } { 7 }$ 
E) None of the above 
A) Ellipse Center: $\frac { 2 } { 7 }$ 
B) Ellipse Center: 1 
C) Circle Radius: 1 
D) Circle Radius: $\frac { 2 } { 7 }$ 
E) None of the above

Question 17

Find the Eccentricity of the conic.​ $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$ ​

Accepted Answer

A) Eccentricity: $e = \frac { \sqrt { 48 } } { 64 }$ 
B) Eccentricity: $e = \frac { \sqrt { 48 } } { 4 }$ 
C) Eccentricity: $e = \frac { \sqrt { 64 } } { 4 }$ 
D) Eccentricity: $e = \frac { \sqrt { 48 } } { 8 }$ 
E) Eccentricity: $e = \frac { \sqrt { 48 } } { 48 }$ 
A) Eccentricity: $e = \frac { \sqrt { 48 } } { 64 }$ 
B) Eccentricity: $e = \frac { \sqrt { 48 } } { 4 }$ 
C) Eccentricity: $e = \frac { \sqrt { 64 } } { 4 }$ 
D) Eccentricity: $e = \frac { \sqrt { 48 } } { 8 }$ 
E) Eccentricity: $e = \frac { \sqrt { 48 } } { 48 }$

Question 18

Find the center and vertices of the ellipse.​ $x ^ { 2 } + 16 y ^ { 2 } - 10 x - 32 y + 25 = 0$ ​

Accepted Answer

A) center: $( 1,5 )$ ;vertices: $( - 3,5 ) , ( 5,5 )$ 
B) center: $( 5,1 )$ ;vertices: $( 1,1 ) , ( 9,1 )$ 
C) center: $( - 5 , - 1 )$ ;vertices: $( - 6 , - 1 ) , ( - 4 , - 1 )$ 
D) center: $( - 5 , - 1 )$ ;vertices: $( - 9 , - 1 ) , ( 1 , - 1 )$ 
E) center: $( 5,1 )$ ;vertices: $( 4,1 ) , ( 6,1 )$ 
A) center: $( 1,5 )$ ;vertices: $( - 3,5 ) , ( 5,5 )$ 
B) center: $( 5,1 )$ ;vertices: $( 1,1 ) , ( 9,1 )$ 
C) center: $( - 5 , - 1 )$ ;vertices: $( - 6 , - 1 ) , ( - 4 , - 1 )$ 
D) center: $( - 5 , - 1 )$ ;vertices: $( - 9 , - 1 ) , ( 1 , - 1 )$ 
E) center: $( 5,1 )$ ;vertices: $( 4,1 ) , ( 6,1 )$

Question 19

Find the standard form of the equation of the ellipse with the given characteristics. ​
​vertices: (-1,-11), (-1,7),minor axis of length 2
​

Accepted Answer

A)  $\frac { ( x + 1 ) ^ { 2 } } { 81 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 81 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 81 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 81 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y - 2 ) ^ { 2 } } { 81 } = 1$ 
A)  $\frac { ( x + 1 ) ^ { 2 } } { 81 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 81 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 2 ) ^ { 2 } } { 81 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 81 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y - 2 ) ^ { 2 } } { 81 } = 1$

Question 20

Write the equation of the ellipse with foci at (2,2), (6,2),and b = 4,where b - semiminor axis. ​

Accepted Answer

A)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = - 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 20 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 20 } = 1$ 
A)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 20 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = - 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 20 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 20 } = 1$

Exam 61: Ellipses

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: (5,3),(5,13)( 5,3 ) , ( 5,13 )(5,3),(5,13) ,endpoints of the major axis: (5,0),(5,16)( 5,0 ) , ( 5,16 )(5,0),(5,16) ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Foci: (±5,0)( \pm 5,0 )(±5,0) ;major axis of length 12 ​

Find the standard form of the equation of the ellipse with the following characteristics. ​ Foci: (±2,0)( \pm 2,0 )(±2,0) ,major axis of length: 22 ​ ​

Find the center and the vertices of the ellipse.​ 81x2+y2=8181 x ^ { 2 } + y ^ { 2 } = 8181x2+y2=81 ​

Find the center and radius of the conic.​ x264+y264=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 164x2​+64y2​=1 ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.​ ​

Select the graph for following equation.​ x29+y216=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 19x2​+16y2​=1 ​

Select the graph for following equation.​ (x+2)29+(y+2)24=1\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 19(x+2)2​+4(y+2)2​=1 ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: (−5,−12),(−5,−4)( - 5 , - 12 ) , ( - 5 , - 4 )(−5,−12),(−5,−4) ,endpoints of the major axis: (−5,−16),(−5,0)( - 5 , - 16 ) , ( - 5,0 )(−5,−16),(−5,0) ​

Find the standard form of the equation of the ellipse with the following characteristics. ​ Foci: (±3,0)( \pm 3,0 )(±3,0) ,major axis of length: 16 ​

Identify the conic as a circle or an ellipse then find the center.​ x29+y24=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 19x2​+4y2​=1 ​

Write the equation of the ellipse that has its center at the origin,focus at (1,0)and vertex at (9,0). ​

Find the center and foci of the ellipse.​ (x−2)245+(y−8)281=1\frac { ( x - 2 ) ^ { 2 } } { 45 } + \frac { ( y - 8 ) ^ { 2 } } { 81 } = 145(x−2)2​+81(y−8)2​=1 ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertices: (0,±8)( 0 , \pm 8 )(0,±8) ;Foci: (0,±4)( 0 , \pm 4 )(0,±4) ​

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse.​ x24/49+(y+1)24/49=1\frac { x ^ { 2 } } { 4 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 49 } = 14/49x2​+4/49(y+1)2​=1 ​

Find the Eccentricity of the conic.​ x264+y216=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 164x2​+16y2​=1 ​

Find the center and vertices of the ellipse.​ x2+16y2−10x−32y+25=0x ^ { 2 } + 16 y ^ { 2 } - 10 x - 32 y + 25 = 0x2+16y2−10x−32y+25=0 ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ ​vertices: (-1,-11), (-1,7),minor axis of length 2 ​

Write the equation of the ellipse with foci at (2,2), (6,2),and b = 4,where b - semiminor axis. ​

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Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( 5,3 ) , ( 5,13 )$ ,endpoints of the major axis: $( 5,0 ) , ( 5,16 )$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: $( \pm 5,0 )$ ;major axis of length 12

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 2,0 )$ ,major axis of length: 22

Find the center and the vertices of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Find the center and radius of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Select the graph for following equation. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Select the graph for following equation. $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( - 5 , - 12 ) , ( - 5 , - 4 )$ ,endpoints of the major axis: $( - 5 , - 16 ) , ( - 5,0 )$

Find the standard form of the equation of the ellipse with the following characteristics. Foci: $( \pm 3,0 )$ ,major axis of length: 16

Identify the conic as a circle or an ellipse then find the center. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Write the equation of the ellipse that has its center at the origin,focus at (1,0)and vertex at (9,0).

Find the center and foci of the ellipse. $\frac { ( x - 2 ) ^ { 2 } } { 45 } + \frac { ( y - 8 ) ^ { 2 } } { 81 } = 1$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: $( 0 , \pm 8 )$ ;Foci: $( 0 , \pm 4 )$

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse. $\frac { x ^ { 2 } } { 4 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 49 } = 1$

Find the Eccentricity of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$

Find the center and vertices of the ellipse. $x ^ { 2 } + 16 y ^ { 2 } - 10 x - 32 y + 25 = 0$

Find the standard form of the equation of the ellipse with the given characteristics. vertices: (-1,-11), (-1,7),minor axis of length 2

Write the equation of the ellipse with foci at (2,2), (6,2),and b = 4,where b - semiminor axis.