Ellipses

Question 1

Written in standard form, what is the equation of the ellipse 25x^2 + 16y^2 - 150x - 64y - 111 = 0?

Accepted Answer

(x - 3)^2/16 + (y - 2)^2/25 = 1

Answer

(x + 3)^2/16 + (y + 2)^2/25 = 1

Answer

(x - 3)^2/25 + (y - 2)^2/16 = 1

Answer

(x - 3)^2/400 + (y - 2)^2/400 = 1

Question 2

For the ellipse x^2/25 + y^2/4 = 1, what are the vertices?

Accepted Answer

(5, 0) and (-5, 0)

Answer

(0, 2) and (0, -2)

Answer

(25, 0) and (-25, 0)

Answer

(0, 5) and (0, -5)

Question 3

For the ellipse x^2/289 + y^2/64 = 1, what are the coordinates of the foci?

Accepted Answer

(15, 0) and (-15, 0)

Answer

(0, 15) and (0, -15)

Answer

(225, 0) and (-225, 0)

Answer

(17, 0) and (-17, 0)

Question 4

The graph shows an ellipse centered at the origin. What is its equation?

Accepted Answer

x^2/16 + y^2/4 = 1

Answer

x^2/4 + y^2/16 = 1

Answer

x^2/4 + y^2/2 = 1

Answer

x^2/16 - y^2/4 = 1

Question 5

Written in standard form, what is the equation of the ellipse 9x^2 + 36y^2 + 54x - 216y + 81 = 0?

Accepted Answer

(x + 3)^2/36 + (y - 3)^2/9 = 1

Answer

(x - 3)^2/36 + (y + 3)^2/9 = 1

Answer

(x + 3)^2/9 + (y - 3)^2/36 = 1

Answer

(x + 3)^2/324 + (y - 3)^2/324 = 1

Question 6

Use the graph of the ellipse. What is its center, and what is the length of its major axis?

Accepted Answer

center (-3, -3), major axis 14

Answer

center (-3, -3), major axis 7

Answer

center (3, 3), major axis 14

Answer

center (-3, -3), major axis 4

Question 7

For the ellipse (x - 6)^2/100 + (y + 1)^2/9 = 1, what is the center and what is the length of the major axis?

Accepted Answer

center (6, -1), major axis 20

Answer

center (6, -1), major axis 10

Answer

center (-6, 1), major axis 20

Answer

center (6, -1), major axis 6

Question 8

An ellipse is centered at the origin with vertices (12, 0) and (-12, 0) and co-vertices (0, 9) and (0, -9). What is its equation?

Accepted Answer

x^2/144 + y^2/81 = 1

Answer

x^2/81 + y^2/144 = 1

Answer

x^2/12 + y^2/9 = 1

Answer

x^2/144 - y^2/81 = 1

Question 9

For the ellipse x^2/81 + y^2/64 = 1, what are the vertices?

Accepted Answer

(9, 0) and (-9, 0)

Answer

(0, 8) and (0, -8)

Answer

(81, 0) and (-81, 0)

Answer

(0, 9) and (0, -9)

Question 10

Use the graph. What are the vertices of the ellipse?

Accepted Answer

(0, 6) and (0, -6)

Answer

(2, 0) and (-2, 0)

Answer

(0, 36) and (0, -36)

Answer

(6, 0) and (-6, 0)

Question 11

The graph shows an ellipse centered at the origin. What is its equation?

Accepted Answer

x^2/81 + y^2/49 = 1

Answer

x^2/49 + y^2/81 = 1

Answer

x^2/9 + y^2/7 = 1

Answer

x^2/81 - y^2/49 = 1

Question 12

Written in standard form, what is the equation of the ellipse 25x^2 + 4y^2 + 250x - 40y + 625 = 0?

Accepted Answer

(x + 5)^2/4 + (y - 5)^2/25 = 1

Answer

(x - 5)^2/4 + (y + 5)^2/25 = 1

Answer

(x + 5)^2/25 + (y - 5)^2/4 = 1

Answer

(x + 5)^2/100 + (y - 5)^2/100 = 1

Question 13

The graph shows an ellipse centered at the origin. What is its equation?

Accepted Answer

x^2/36 + y^2/16 = 1

Answer

x^2/16 + y^2/36 = 1

Answer

x^2/6 + y^2/4 = 1

Answer

x^2/36 - y^2/16 = 1

Question 14

An ellipse is centered at the origin with vertices (12, 0) and (-12, 0) and co-vertices (0, 6) and (0, -6). What is its equation?

Accepted Answer

x^2/144 + y^2/36 = 1

Answer

x^2/36 + y^2/144 = 1

Answer

x^2/12 + y^2/6 = 1

Answer

x^2/144 - y^2/36 = 1

Question 15

For the ellipse (x + 5)^2/144 + (y + 1)^2/49 = 1, what is the center and what is the length of the major axis?

Accepted Answer

center (-5, -1), major axis 24

Answer

center (-5, -1), major axis 12

Answer

center (5, 1), major axis 24

Answer

center (-5, -1), major axis 14

Question 16

For the ellipse (x - 6)^2/81 + (y - 1)^2/4 = 1, what is the center and what is the length of the major axis?

Accepted Answer

center (6, 1), major axis 18

Answer

center (6, 1), major axis 9

Answer

center (-6, -1), major axis 18

Answer

center (6, 1), major axis 4

Question 17

Use the graph of the ellipse. What are the coordinates of its foci?

Accepted Answer

(6, 0) and (-6, 0)

Answer

(0, 6) and (0, -6)

Answer

(36, 0) and (-36, 0)

Answer

(10, 0) and (-10, 0)

Question 18

For the ellipse (x - 4)^2/64 + (y - 4)^2/81 = 1, what is the center and what is the length of the major axis?

Accepted Answer

center (4, 4), major axis 18

Answer

center (4, 4), major axis 9

Answer

center (-4, -4), major axis 18

Answer

center (4, 4), major axis 16

Question 19

For the ellipse x^2/64 + y^2/81 = 1, what are the vertices?

Accepted Answer

(0, 9) and (0, -9)

Answer

(8, 0) and (-8, 0)

Answer

(0, 81) and (0, -81)

Answer

(9, 0) and (-9, 0)

Question 20

For the ellipse x^2/9 + y^2/64 = 1, what are the vertices?

Accepted Answer

(0, 8) and (0, -8)

Answer

(3, 0) and (-3, 0)

Answer

(0, 64) and (0, -64)

Answer

(8, 0) and (-8, 0)

Question 21

An ellipse is centered at the origin with vertices (10, 0) and (-10, 0) and co-vertices (0, 2) and (0, -2). What is its equation?

Accepted Answer

x^2/100 + y^2/4 = 1

Answer

x^2/4 + y^2/100 = 1

Answer

x^2/10 + y^2/2 = 1

Answer

x^2/100 - y^2/4 = 1

Question 22

Written in standard form, what is the equation of the ellipse 9x^2 + 16y^2 + 54x + 96y + 81 = 0?

Accepted Answer

(x + 3)^2/16 + (y + 3)^2/9 = 1

Answer

(x - 3)^2/16 + (y - 3)^2/9 = 1

Answer

(x + 3)^2/9 + (y + 3)^2/16 = 1

Answer

(x + 3)^2/144 + (y + 3)^2/144 = 1

Question 23

For the ellipse x^2/64 + y^2/25 = 1, what are the vertices?

Accepted Answer

(8, 0) and (-8, 0)

Answer

(0, 5) and (0, -5)

Answer

(64, 0) and (-64, 0)

Answer

(0, 8) and (0, -8)

Question 24

Use the graph of the ellipse. What is its center, and what is the length of its major axis?

Accepted Answer

center (-6, -5), major axis 12

Answer

center (-6, -5), major axis 6

Answer

center (6, 5), major axis 12

Answer

center (-6, -5), major axis 4

Question 25

For the ellipse x^2/625 + y^2/49 = 1, what are the coordinates of the foci?

Accepted Answer

(24, 0) and (-24, 0)

Answer

(0, 24) and (0, -24)

Answer

(576, 0) and (-576, 0)

Answer

(25, 0) and (-25, 0)

Question 26

Use the graph. What are the vertices of the ellipse?

Accepted Answer

(0, 5) and (0, -5)

Answer

(3, 0) and (-3, 0)

Answer

(0, 25) and (0, -25)

Answer

(5, 0) and (-5, 0)

Question 27

The graph shows an ellipse centered at the origin. What is its equation?

Accepted Answer

x^2/144 + y^2/64 = 1

Answer

x^2/64 + y^2/144 = 1

Answer

x^2/12 + y^2/8 = 1

Answer

x^2/144 - y^2/64 = 1

Question 28

For the ellipse (x + 6)^2/64 + (y - 4)^2/49 = 1, what is the center and what is the length of the major axis?

Accepted Answer

center (-6, 4), major axis 16

Answer

center (-6, 4), major axis 8

Answer

center (6, -4), major axis 16

Answer

center (-6, 4), major axis 14

Question 29

For the ellipse x^2/4 + y^2/49 = 1, what are the vertices?

Accepted Answer

(0, 7) and (0, -7)

Answer

(2, 0) and (-2, 0)

Answer

(0, 49) and (0, -49)

Answer

(7, 0) and (-7, 0)

Question 30

For the ellipse x^2/625 + y^2/576 = 1, what are the coordinates of the foci?

Accepted Answer

(7, 0) and (-7, 0)

Answer

(0, 7) and (0, -7)

Answer

(49, 0) and (-49, 0)

Answer

(25, 0) and (-25, 0)

Question 31

For the ellipse x^2/49 + y^2/81 = 1, what are the vertices?

Accepted Answer

(0, 9) and (0, -9)

Answer

(7, 0) and (-7, 0)

Answer

(0, 81) and (0, -81)

Answer

(9, 0) and (-9, 0)

Question 32

The graph shows an ellipse centered at the origin. What is its equation?

Accepted Answer

x^2/49 + y^2/4 = 1

Answer

x^2/4 + y^2/49 = 1

Answer

x^2/7 + y^2/2 = 1

Answer

x^2/49 - y^2/4 = 1

Question 33

Use the graph of the ellipse. What is its center, and what is the length of its major axis?

Accepted Answer

center (-3, -1), major axis 18

Answer

center (-3, -1), major axis 9

Answer

center (3, 1), major axis 18

Answer

center (-3, -1), major axis 10

Question 34

Written in standard form, what is the equation of the ellipse 16x^2 + 36y^2 - 160x + 288y + 400 = 0?

Accepted Answer

(x - 5)^2/36 + (y + 4)^2/16 = 1

Answer

(x + 5)^2/36 + (y - 4)^2/16 = 1

Answer

(x - 5)^2/16 + (y + 4)^2/36 = 1

Answer

(x - 5)^2/576 + (y + 4)^2/576 = 1

Question 35

For the ellipse x^2/169 + y^2/144 = 1, what are the coordinates of the foci?

Accepted Answer

(5, 0) and (-5, 0)

Answer

(0, 5) and (0, -5)

Answer

(25, 0) and (-25, 0)

Answer

(13, 0) and (-13, 0)

Question 36

Written in standard form, what is the equation of the ellipse 4x^2 + 9y^2 - 48x - 72y + 252 = 0?

Accepted Answer

(x - 6)^2/9 + (y - 4)^2/4 = 1

Answer

(x + 6)^2/9 + (y + 4)^2/4 = 1

Answer

(x - 6)^2/4 + (y - 4)^2/9 = 1

Answer

(x - 6)^2/36 + (y - 4)^2/36 = 1

Question 37

For the ellipse x^2/36 + y^2/16 = 1, what are the vertices?

Accepted Answer

(6, 0) and (-6, 0)

Answer

(0, 4) and (0, -4)

Answer

(36, 0) and (-36, 0)

Answer

(0, 6) and (0, -6)

Question 38

Use the graph of the ellipse. What are the coordinates of its foci?

Accepted Answer

(3, 0) and (-3, 0)

Answer

(0, 3) and (0, -3)

Answer

(9, 0) and (-9, 0)

Answer

(5, 0) and (-5, 0)

Question 39

For the ellipse (x + 6)^2/100 + (y - 6)^2/9 = 1, what is the center and what is the length of the major axis?

Accepted Answer

center (-6, 6), major axis 20

Answer

center (-6, 6), major axis 10

Answer

center (6, -6), major axis 20

Answer

center (-6, 6), major axis 6

Question 40

For the ellipse (x - 5)^2/144 + (y - 1)^2/25 = 1, what is the center and what is the length of the major axis?

Accepted Answer

center (5, 1), major axis 24

Answer

center (5, 1), major axis 12

Answer

center (-5, -1), major axis 24

Answer

center (5, 1), major axis 10

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Ellipses

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Board Games: Teacher-led, projected to the class

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Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner

Ellipses

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner