Question 1

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

Accepted Answer

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

Question 2

Find the standard form of the equation of the ellipse with vertices $( 0 , \pm 9 )$ and eccentricity $e = \frac { 3 } { 9 }$ .

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 81 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 72 } = 1$ 
E)  $\frac { x ^ { 2 } } { 72 } + \frac { y ^ { 2 } } { 81 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 81 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 72 } = 1$ 
E)  $\frac { x ^ { 2 } } { 72 } + \frac { y ^ { 2 } } { 81 } = 1$

Question 3

Identify the conic by writing the equation in standard form.​ $18 y ^ { 2 } - 24 x ^ { 2 } + 216 y + 336 x - 543 = 0$ ​

Accepted Answer

A) ​ $\frac { ( y - 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ;ellipse 
B) ​ $\frac { ( y + 6 ) ^ { 2 } } { \frac { 97 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 97 } { 8 } } = 1$ ;hyperbola 
C) ​ $\frac { ( y - 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ;hyperbola 
D) ​ $\frac { ( y + 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ;hyperbola 
E) ​ $\frac { ( y + 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ;ellipse 
A) ​ $\frac { ( y - 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ;ellipse 
B) ​ $\frac { ( y + 6 ) ^ { 2 } } { \frac { 97 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 97 } { 8 } } = 1$ ;hyperbola 
C) ​ $\frac { ( y - 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ;hyperbola 
D) ​ $\frac { ( y + 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ;hyperbola 
E) ​ $\frac { ( y + 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ;ellipse

Question 4

Find the standard form of the equation of the ellipse with the given characteristics. ​
Center: $( 0,4 )$ ;a = 2c;Vertices: $( - 8,8 ) , ( 8,8 )$ ,where a - thr semimajor axis,b - semiminor axis and $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ .
​

Accepted Answer

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

Question 5

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci: $( 7 , - 7 ) , ( 7 , - 1 )$ ,endpoints of the major axis: $( 7 , - 13 ) , ( 7,5 )$ ​

Accepted Answer

A)  $\frac { ( x + 7 ) ^ { 2 } } { 72 } + \frac { ( y - 4 ) ^ { 2 } } { 81 } = 1$ 
B)  $\frac { ( x - 7 ) ^ { 2 } } { 72 } + \frac { ( y + 4 ) ^ { 2 } } { 81 } = 1$ 
C)  $\frac { ( x - 7 ) ^ { 2 } } { 81 } + \frac { ( y + 4 ) ^ { 2 } } { 72 } = 1$ 
D)  $\frac { ( x - 7 ) ^ { 2 } } { 72 } + \frac { ( y + 4 ) ^ { 2 } } { 81 } = - 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { 81 } + \frac { ( y + 7 ) ^ { 2 } } { 72 } = 1$ 
A)  $\frac { ( x + 7 ) ^ { 2 } } { 72 } + \frac { ( y - 4 ) ^ { 2 } } { 81 } = 1$ 
B)  $\frac { ( x - 7 ) ^ { 2 } } { 72 } + \frac { ( y + 4 ) ^ { 2 } } { 81 } = 1$ 
C)  $\frac { ( x - 7 ) ^ { 2 } } { 81 } + \frac { ( y + 4 ) ^ { 2 } } { 72 } = 1$ 
D)  $\frac { ( x - 7 ) ^ { 2 } } { 72 } + \frac { ( y + 4 ) ^ { 2 } } { 81 } = - 1$ 
E)  $\frac { ( x - 4 ) ^ { 2 } } { 81 } + \frac { ( y + 7 ) ^ { 2 } } { 72 } = 1$

Question 6

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertices: $( \pm 7,0 )$ ;Foci: $( \pm 5,0 )$ ​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 24 } = 1$ 
B)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$ 
A)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 24 } = 1$ 
B)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$

Question 7

Select the graph for following equation.​ $$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$$ ​

Accepted Answer

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

Question 8

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

Accepted Answer

A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) Circle Center: (7,0) 
D) Ellipse Center: (0,7) 
E) ​Circle Center: (7,7) 
A) Circle Center: (0,0) 
B) Ellipse Center: (0,0) 
C) Circle Center: (7,0) 
D) Ellipse Center: (0,7) 
E) ​Circle Center: (7,7)

Question 9

The first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957).Its highest point above Earths surface was 943 kilometers,and its lowest point was 211 kilometers (see figure).The center of Earth was at one focus of the elliptical orbit,and the radius of Earth is 6392 kilometers.Find the eccentricity of the orbit.Round your results to four decimal place.​   ​ $$x = 211 \mathrm {~km} , y = 943 \mathrm {~km}$$ ​

Accepted Answer

A) Eccentricity: $e \approx 0.4555$ 
B) Eccentricity: $e \approx 0.4755$ 
C) Eccentricity: $e \approx 0.4955$ 
D) Eccentricity: $e \approx 0.4355$ 
E) Eccentricity: $e \approx 0.5155$ 
A) Eccentricity: $e \approx 0.4555$ 
B) Eccentricity: $e \approx 0.4755$ 
C) Eccentricity: $e \approx 0.4955$ 
D) Eccentricity: $e \approx 0.4355$ 
E) Eccentricity: $e \approx 0.5155$

Question 10

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

Accepted Answer

A) Foci: $( 0 , \pm \sqrt { 48 } )$ 
B) Foci: $( \pm \sqrt { 8 } , 0 )$ 
C) Foci: $( 0 , \pm \sqrt { 8 } )$ 
D) Foci: $( \pm \sqrt { 48 } , 0 )$ 
E) Foci: $( \sqrt { 8 } , \sqrt { 48 } )$ 
A) Foci: $( 0 , \pm \sqrt { 48 } )$ 
B) Foci: $( \pm \sqrt { 8 } , 0 )$ 
C) Foci: $( 0 , \pm \sqrt { 8 } )$ 
D) Foci: $( \pm \sqrt { 48 } , 0 )$ 
E) Foci: $( \sqrt { 8 } , \sqrt { 48 } )$

Question 11

Find the standard form of the equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 7 } { 9 }$ .

Accepted Answer

A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 32 } = 1$ 
D)  $\frac { x ^ { 2 } } { 32 } + \frac { y ^ { 2 } } { 81 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 81 } = 1$ 
A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 32 } = 1$ 
D)  $\frac { x ^ { 2 } } { 32 } + \frac { y ^ { 2 } } { 81 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 81 } = 1$

Question 12

Identify the conic by writing the equation in standard form.​ $4 x ^ { 2 } + 9 y ^ { 2 } + 40 x + 54 y + 145 = 0$ ​

Accepted Answer

A)  $\frac { ( x + 5 ) ^ { 2 } } { 9 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ ;ellipse 
B)  $( 3 x + 5 ) ^ { 2 } + ( 2 y + 1 ) ^ { 2 } = 167$ ;circle 
C)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 422 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 211 } { 2 } } = 1$ ;ellipse 
D)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 73 } { 3 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 219 } { 4 } } = 1$ ;ellipse 
E)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 167 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 167 } { 4 } } = 1$ ;ellipse 
A)  $\frac { ( x + 5 ) ^ { 2 } } { 9 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ ;ellipse 
B)  $( 3 x + 5 ) ^ { 2 } + ( 2 y + 1 ) ^ { 2 } = 167$ ;circle 
C)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 422 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 211 } { 2 } } = 1$ ;ellipse 
D)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 73 } { 3 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 219 } { 4 } } = 1$ ;ellipse 
E)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 167 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 167 } { 4 } } = 1$ ;ellipse

Question 13

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertical major axis passes through the points $( 0,7 ) \text { and } ( 5,0 )$ .
​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$

Question 14

Find the center and vertices of the ellipse.​ $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$ ​

Accepted Answer

A) center: (8,6)vertices: (-8,-6), (8,6) 
B) center: (0,0)vertices: (0,-8), (0,8) 
C) center: (0,0)vertices: (-8,0), (8,0) 
D) center: (8,0)vertices: (0,-6), (0,6) 
E) center: (0,0)vertices: (-6,0), (6,0) 
A) center: (8,6)vertices: (-8,-6), (8,6) 
B) center: (0,0)vertices: (0,-8), (0,8) 
C) center: (0,0)vertices: (-8,0), (8,0) 
D) center: (8,0)vertices: (0,-6), (0,6) 
E) center: (0,0)vertices: (-6,0), (6,0)

Question 15

Identify the graph of the following ellipse.​ $$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$$ ​

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
A)    ​ 
B)    ​ 
C)    ​

Question 16

Find the center and vertices of the ellipse.​ $x ^ { 2 } + 4 y ^ { 2 } - 6 x + 8 y + 9 = 0$ ​

Accepted Answer

A) center: (-1,3),vertices: (-3,3), (1,3) 
B) center: (-3,1),vertices: (-4,1), (-2,1) 
C) center: (3,-1),vertices: (2,-1), (4,-1) 
D) center: (3,-1),vertices: (1,-1), (5,-1) 
E) center: (-3,1),vertices: (-5,1), (-1,1) 
A) center: (-1,3),vertices: (-3,3), (1,3) 
B) center: (-3,1),vertices: (-4,1), (-2,1) 
C) center: (3,-1),vertices: (2,-1), (4,-1) 
D) center: (3,-1),vertices: (1,-1), (5,-1) 
E) center: (-3,1),vertices: (-5,1), (-1,1)

Question 17

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

Accepted Answer

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

Question 18

Any sound from one focus of an ellipse reflects off the ellipse directly back to the other focus.This property explains whispering galleries such as Statuary Hall in Washington,D.C.The whispering gallery shown in illustration has the shape of a semi-circle.Find the distance sound travels as it leaves focus F and returns to focus F'.Round your answer to one decimal place,if necessary.​   ​

Accepted Answer

A) 16 meters 
B) 16.8 meters 
C) 33.5 meters 
D) 32 meters 
E) 31.2 meters 
A) 16 meters 
B) 16.8 meters 
C) 33.5 meters 
D) 32 meters 
E) 31.2 meters

Question 19

Find the eccentricity of the ellipse.​ $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$ ​

Accepted Answer

A) Eccentricity: $e = \frac { 8 \sqrt { 17 } } { 17 }$ 
B) Eccentricity: $e = \frac { \sqrt { 17 } } { 9 }$ 
C) Eccentricity: $$e = - \frac { \sqrt { 17 } } { 9 }$$ 
D) Eccentricity: $$e = \frac { \sqrt { 17 } } { 17 }$$ 
E) Eccentricity: $e = - \frac { 9 \sqrt { 17 } } { 9 }$ 
A) Eccentricity: $e = \frac { 8 \sqrt { 17 } } { 17 }$ 
B) Eccentricity: $e = \frac { \sqrt { 17 } } { 9 }$ 
C) Eccentricity: $$e = - \frac { \sqrt { 17 } } { 9 }$$ 
D) Eccentricity: $$e = \frac { \sqrt { 17 } } { 17 }$$ 
E) Eccentricity: $e = - \frac { 9 \sqrt { 17 } } { 9 }$

Question 20

Find the center and foci of the ellipse.​ $\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$ ​

Accepted Answer

A) center: $( 1 , - 5 )$ foci: $( 1,4 ) , ( 1 , - 2 )$ 
B) center: $( - 1,5 )$ foci: $( 8,5 ) , ( 2,5 )$ 
C) center: $( - 1,5 )$ foci: $( - 1,2 ) , ( - 1,8 )$ 
D) center: $( - 1,5 )$ foci: $( - 2 , - 5 ) , ( 4 , - 5 )$ 
E) center: $( 1 , - 5 )$ foci: $( - 2,5 ) , ( 4,5 )$ 
A) center: $( 1 , - 5 )$ foci: $( 1,4 ) , ( 1 , - 2 )$ 
B) center: $( - 1,5 )$ foci: $( 8,5 ) , ( 2,5 )$ 
C) center: $( - 1,5 )$ foci: $( - 1,2 ) , ( - 1,8 )$ 
D) center: $( - 1,5 )$ foci: $( - 2 , - 5 ) , ( 4 , - 5 )$ 
E) center: $( 1 , - 5 )$ foci: $( - 2,5 ) , ( 4,5 )$

Exam 61: Ellipses

Select the graph for following equation.​ (x−2)216+(y+1)2=1\frac { ( x - 2 ) ^ { 2 } } { 16 } + ( y + 1 ) ^ { 2 } = 116(x−2)2​+(y+1)2=1 ​

Find the standard form of the equation of the ellipse with vertices (0,±9)( 0 , \pm 9 )(0,±9) and eccentricity e=39e = \frac { 3 } { 9 }e=93​ .

Identify the conic by writing the equation in standard form.​ 18y2−24x2+216y+336x−543=018 y ^ { 2 } - 24 x ^ { 2 } + 216 y + 336 x - 543 = 018y2−24x2+216y+336x−543=0 ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Center: (0,4)( 0,4 )(0,4) ;a = 2c;Vertices: (−8,8),(8,8)( - 8,8 ) , ( 8,8 )(−8,8),(8,8) ,where a - thr semimajor axis,b - semiminor axis and c2=a2−b2c ^ { 2 } = a ^ { 2 } - b ^ { 2 }c2=a2−b2 . ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Foci: (7,−7),(7,−1)( 7 , - 7 ) , ( 7 , - 1 )(7,−7),(7,−1) ,endpoints of the major axis: (7,−13),(7,5)( 7 , - 13 ) , ( 7,5 )(7,−13),(7,5) ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertices: (±7,0)( \pm 7,0 )(±7,0) ;Foci: (±5,0)( \pm 5,0 )(±5,0) ​

Select the graph for following equation.​ x225+y216=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 125x2​+16y2​=1 ​

Identify the conic as a circle or an ellipse then find the center.​ x249+y249=1\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 49 } = 149x2​+49y2​=1 ​

Find the Foci of the conic.​ x216+y264=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 116x2​+64y2​=1 ​

Find the standard form of the equation of the ellipse with vertices (±9,0)( \pm 9,0 )(±9,0) and eccentricity e=79e = \frac { 7 } { 9 }e=97​ .

Identify the conic by writing the equation in standard form.​ 4x2+9y2+40x+54y+145=04 x ^ { 2 } + 9 y ^ { 2 } + 40 x + 54 y + 145 = 04x2+9y2+40x+54y+145=0 ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertical major axis passes through the points (0,7) and (5,0)( 0,7 ) \text { and } ( 5,0 )(0,7) and (5,0) . ​

Find the center and vertices of the ellipse.​ x264+y236=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 164x2​+36y2​=1 ​

Identify the graph of the following ellipse.​ x236+y24=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 136x2​+4y2​=1 ​

Find the center and vertices of the ellipse.​ x2+4y2−6x+8y+9=0x ^ { 2 } + 4 y ^ { 2 } - 6 x + 8 y + 9 = 0x2+4y2−6x+8y+9=0 ​

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

Find the eccentricity of the ellipse.​ x264+y281=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 164x2​+81y2​=1 ​

Find the center and foci of the ellipse.​ (x+1)27+(y−5)216=1\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 17(x+1)2​+16(y−5)2​=1 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

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Linear Programming

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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

Hyperbolas

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

Find the standard form of the equation of the ellipse with vertices $( 0 , \pm 9 )$ and eccentricity $e = \frac { 3 } { 9 }$ .

Identify the conic by writing the equation in standard form. $18 y ^ { 2 } - 24 x ^ { 2 } + 216 y + 336 x - 543 = 0$

Find the standard form of the equation of the ellipse with the given characteristics. Center: $( 0,4 )$ ;a = 2c;Vertices: $( - 8,8 ) , ( 8,8 )$ ,where a - thr semimajor axis,b - semiminor axis and $c ^ { 2 } = a ^ { 2 } - b ^ { 2 }$ .

Find the standard form of the equation of the ellipse with the given characteristics. Foci: $( 7 , - 7 ) , ( 7 , - 1 )$ ,endpoints of the major axis: $( 7 , - 13 ) , ( 7,5 )$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: $( \pm 7,0 )$ ;Foci: $( \pm 5,0 )$

Select the graph for following equation. $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$

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

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

Find the standard form of the equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 7 } { 9 }$ .

Identify the conic by writing the equation in standard form. $4 x ^ { 2 } + 9 y ^ { 2 } + 40 x + 54 y + 145 = 0$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis passes through the points $( 0,7 ) \text { and } ( 5,0 )$ .

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$

Identify the graph of the following ellipse. $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 4 } = 1$

Find the center and vertices of the ellipse. $x ^ { 2 } + 4 y ^ { 2 } - 6 x + 8 y + 9 = 0$

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

Find the eccentricity of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = 1$

Find the center and foci of the ellipse. $\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$