Hyperbolas

Question 1

For (y + 5)^2/25 - (x - 2)^2/9 = 1, a student reports vertices at (5, -5) and (-1, -5), taking the transverse axis to be horizontal. What are the correct vertices?

Accepted Answer

(2, 0) and (2, -10)

Answer

(5, -5) and (-1, -5)

Answer

(2, 20) and (2, -30)

Answer

(-5, 7) and (5, -3)

Question 2

For the hyperbola (y - 4)^2/36 - (x + 5)^2/81 = 1, what are the center and the vertices?

Accepted Answer

center (-5, 4), vertices (-5, 10) and (-5, -2)

Answer

center (-5, 4), vertices (4, 4) and (-14, 4)

Answer

center (5, -4), vertices (5, 2) and (5, -10)

Answer

center (-5, 4), vertices (-5, 40) and (-5, -32)

Question 3

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

For the hyperbola x^2/400 - y^2/441 = 1, what are the coordinates of the foci?

Accepted Answer

(29, 0) and (-29, 0)

Answer

(0, 29) and (0, -29)

Answer

(41, 0) and (-41, 0)

Answer

(20, 0) and (-20, 0)

Question 5

For the hyperbola x^2/64 - y^2/225 = 1, what are the coordinates of the foci?

Accepted Answer

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

Answer

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

Answer

(23, 0) and (-23, 0)

Answer

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

Question 6

Use the graph. What are the asymptotes of the hyperbola?

Accepted Answer

y = (5/3)x and y = -(5/3)x

Answer

y = (3/5)x and y = -(3/5)x

Answer

y = (25/9)x and y = -(25/9)x

Answer

y = (5/3)x and y = (3/5)x

Question 7

What are the asymptotes of the hyperbola x^2/16 - y^2/81 = 1?

Accepted Answer

y = (9/4)x and y = -(9/4)x

Answer

y = (4/9)x and y = -(4/9)x

Answer

y = (81/16)x and y = -(81/16)x

Answer

y = (9/4)x and y = (4/9)x

Question 8

For the hyperbola (x - 3)^2/100 - (y - 6)^2/16 = 1, what are the center and the vertices?

Accepted Answer

center (3, 6), vertices (13, 6) and (-7, 6)

Answer

center (3, 6), vertices (3, 10) and (3, 2)

Answer

center (-3, -6), vertices (7, -6) and (-13, -6)

Answer

center (3, 6), vertices (103, 6) and (-97, 6)

Question 9

Use the graph. What are the asymptotes of the hyperbola?

Accepted Answer

y = (4/3)x and y = -(4/3)x

Answer

y = (3/4)x and y = -(3/4)x

Answer

y = (16/9)x and y = -(16/9)x

Answer

y = (4/3)x and y = (3/4)x

Question 10

A hyperbola is centered at the origin with vertices (0, 9) and (0, -9), and its asymptotes have slopes 9/7 and -9/7. What is its equation?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

For the hyperbola (x + 4)^2/16 - (y + 5)^2/9 = 1, what are the center and the vertices?

Accepted Answer

center (-4, -5), vertices (0, -5) and (-8, -5)

Answer

center (-4, -5), vertices (-4, -2) and (-4, -8)

Answer

center (4, 5), vertices (8, 5) and (0, 5)

Answer

center (-4, -5), vertices (12, -5) and (-20, -5)

Question 12

For the hyperbola (x - 2)^2/49 - (y + 2)^2/81 = 1, what are the center and the vertices?

Accepted Answer

center (2, -2), vertices (9, -2) and (-5, -2)

Answer

center (2, -2), vertices (2, 7) and (2, -11)

Answer

center (-2, 2), vertices (5, 2) and (-9, 2)

Answer

center (2, -2), vertices (51, -2) and (-47, -2)

Question 13

Use the graph. What are the asymptotes of the hyperbola?

Accepted Answer

y = (1/2)x and y = -(1/2)x

Answer

y = (2)x and y = -(2)x

Answer

y = (1/4)x and y = -(1/4)x

Answer

y = (1/2)x and y = (2)x

Question 14

Use the graph. What are the asymptotes of the hyperbola?

Accepted Answer

y = (3/5)x and y = -(3/5)x

Answer

y = (5/3)x and y = -(5/3)x

Answer

y = (9/25)x and y = -(9/25)x

Answer

y = (3/5)x and y = (5/3)x

Question 15

Use the graph. What is the equation of the hyperbola?

Accepted Answer

y^2/64 - x^2/9 = 1

Answer

x^2/64 - y^2/9 = 1

Answer

y^2/9 - x^2/64 = 1

Answer

y^2/64 + x^2/9 = 1

Question 16

For the hyperbola (x - 2)^2/81 - (y - 3)^2/36 = 1, what are the center and the vertices?

Accepted Answer

center (2, 3), vertices (11, 3) and (-7, 3)

Answer

center (2, 3), vertices (2, 9) and (2, -3)

Answer

center (-2, -3), vertices (7, -3) and (-11, -3)

Answer

center (2, 3), vertices (83, 3) and (-79, 3)

Question 17

What are the asymptotes of the hyperbola y^2/16 - x^2/81 = 1?

Accepted Answer

y = (4/9)x and y = -(4/9)x

Answer

y = (9/4)x and y = -(9/4)x

Answer

y = (16/81)x and y = -(16/81)x

Answer

y = (4/9)x and y = (9/4)x

Question 18

Use the graph of the hyperbola. What are its center and its vertices?

Accepted Answer

center (4, -1), vertices (4, 2) and (4, -4)

Answer

center (4, -1), vertices (11, -1) and (-3, -1)

Answer

center (-4, 1), vertices (-4, 4) and (-4, -2)

Answer

center (4, -1), vertices (4, 8) and (4, -10)

Question 19

Use the graph. What is the equation of the hyperbola?

Accepted Answer

y^2/25 - x^2/4 = 1

Answer

x^2/25 - y^2/4 = 1

Answer

y^2/4 - x^2/25 = 1

Answer

y^2/25 + x^2/4 = 1

Question 20

What are the asymptotes of the hyperbola y^2/25 - x^2/4 = 1?

Accepted Answer

y = (5/2)x and y = -(5/2)x

Answer

y = (2/5)x and y = -(2/5)x

Answer

y = (25/4)x and y = -(25/4)x

Answer

y = (5/2)x and y = (2/5)x

Question 21

What are the asymptotes of the hyperbola y^2/25 - x^2/9 = 1?

Accepted Answer

y = (5/3)x and y = -(5/3)x

Answer

y = (3/5)x and y = -(3/5)x

Answer

y = (25/9)x and y = -(25/9)x

Answer

y = (5/3)x and y = (3/5)x

Question 22

For (y - 6)^2/81 - (x - 2)^2/4 = 1, a student reports vertices at (4, 6) and (0, 6), taking the transverse axis to be horizontal. What are the correct vertices?

Accepted Answer

(2, 15) and (2, -3)

Answer

(4, 6) and (0, 6)

Answer

(2, 87) and (2, -75)

Answer

(6, 11) and (-6, -7)

Question 23

For (y - 3)^2/81 - (x + 4)^2/25 = 1, a student reports vertices at (1, 3) and (-9, 3), taking the transverse axis to be horizontal. What are the correct vertices?

Accepted Answer

(-4, 12) and (-4, -6)

Answer

(1, 3) and (-9, 3)

Answer

(-4, 84) and (-4, -78)

Answer

(3, 5) and (-3, -13)

Question 24

For the hyperbola x^2/36 - y^2/64 = 1, what are the coordinates of the foci?

Accepted Answer

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

Answer

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

Answer

(14, 0) and (-14, 0)

Answer

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

Question 25

For (y - 4)^2/16 - (x - 5)^2/4 = 1, a student reports vertices at (7, 4) and (3, 4), taking the transverse axis to be horizontal. What are the correct vertices?

Accepted Answer

(5, 8) and (5, 0)

Answer

(7, 4) and (3, 4)

Answer

(5, 20) and (5, -12)

Answer

(4, 9) and (-4, 1)

Question 26

Use the graph of the hyperbola. What are its center and its vertices?

Accepted Answer

center (-2, -1), vertices (-2, 1) and (-2, -3)

Answer

center (-2, -1), vertices (5, -1) and (-9, -1)

Answer

center (2, 1), vertices (2, 3) and (2, -1)

Answer

center (-2, -1), vertices (-2, 3) and (-2, -5)

Question 27

What are the asymptotes of the hyperbola x^2/36 - y^2/81 = 1?

Accepted Answer

y = (3/2)x and y = -(3/2)x

Answer

y = (2/3)x and y = -(2/3)x

Answer

y = (9/4)x and y = -(9/4)x

Answer

y = (3/2)x and y = (2/3)x

Question 28

Use the graph. What is the equation of the hyperbola?

Accepted Answer

y^2/25 - x^2/9 = 1

Answer

x^2/25 - y^2/9 = 1

Answer

y^2/9 - x^2/25 = 1

Answer

y^2/25 + x^2/9 = 1

Question 29

For the hyperbola (y - 3)^2/49 - (x + 5)^2/81 = 1, what are the center and the vertices?

Accepted Answer

center (-5, 3), vertices (-5, 10) and (-5, -4)

Answer

center (-5, 3), vertices (4, 3) and (-14, 3)

Answer

center (5, -3), vertices (5, 4) and (5, -10)

Answer

center (-5, 3), vertices (-5, 52) and (-5, -46)

Question 30

What are the asymptotes of the hyperbola x^2/64 - y^2/4 = 1?

Accepted Answer

y = (1/4)x and y = -(1/4)x

Answer

y = 4x and y = -4x

Answer

y = (1/16)x and y = -(1/16)x

Answer

y = (1/4)x and y = 4x

Question 31

A hyperbola is centered at the origin with vertices (0, 9) and (0, -9), and its asymptotes have slopes 9/5 and -9/5. What is its equation?

Accepted Answer

y^2/81 - x^2/25 = 1

Answer

x^2/81 - y^2/25 = 1

Answer

y^2/25 - x^2/81 = 1

Answer

y^2/81 + x^2/25 = 1

Question 32

A hyperbola is centered at the origin with vertices (0, 9) and (0, -9), and its asymptotes have slopes 9/8 and -9/8. What is its equation?

Accepted Answer

y^2/81 - x^2/64 = 1

Answer

x^2/81 - y^2/64 = 1

Answer

y^2/64 - x^2/81 = 1

Answer

y^2/81 + x^2/64 = 1

Question 33

For the hyperbola (x - 2)^2/4 - (y - 6)^2/81 = 1, what are the center and the vertices?

Accepted Answer

center (2, 6), vertices (4, 6) and (0, 6)

Answer

center (2, 6), vertices (2, 15) and (2, -3)

Answer

center (-2, -6), vertices (0, -6) and (-4, -6)

Answer

center (2, 6), vertices (6, 6) and (-2, 6)

Question 34

A hyperbola is centered at the origin with vertices (0, 10) and (0, -10), and its asymptotes have slopes 10/3 and -10/3. What is its equation?

Accepted Answer

y^2/100 - x^2/9 = 1

Answer

x^2/100 - y^2/9 = 1

Answer

y^2/9 - x^2/100 = 1

Answer

y^2/100 + x^2/9 = 1

Question 35

For the hyperbola (x - 4)^2/49 - (y - 1)^2/36 = 1, what are the center and the vertices?

Accepted Answer

center (4, 1), vertices (11, 1) and (-3, 1)

Answer

center (4, 1), vertices (4, 7) and (4, -5)

Answer

center (-4, -1), vertices (3, -1) and (-11, -1)

Answer

center (4, 1), vertices (53, 1) and (-45, 1)

Question 36

Use the graph of the hyperbola. What are its center and its vertices?

Accepted Answer

center (4, 6), vertices (4, 9) and (4, 3)

Answer

center (4, 6), vertices (9, 6) and (-1, 6)

Answer

center (-4, -6), vertices (-4, -3) and (-4, -9)

Answer

center (4, 6), vertices (4, 15) and (4, -3)

Question 37

Use the graph. What is the equation of the hyperbola?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 38

For the hyperbola (y - 2)^2/49 - (x - 6)^2/16 = 1, what are the center and the vertices?

Accepted Answer

center (6, 2), vertices (6, 9) and (6, -5)

Answer

center (6, 2), vertices (10, 2) and (2, 2)

Answer

center (-6, -2), vertices (-6, 5) and (-6, -9)

Answer

center (6, 2), vertices (6, 51) and (6, -47)

Question 39

What are the asymptotes of the hyperbola y^2/81 - x^2/64 = 1?

Accepted Answer

y = (9/8)x and y = -(9/8)x

Answer

y = (8/9)x and y = -(8/9)x

Answer

y = (81/64)x and y = -(81/64)x

Answer

y = (9/8)x and y = (8/9)x

Question 40

What are the asymptotes of the hyperbola x^2/100 - y^2/4 = 1?

Accepted Answer

y = (1/5)x and y = -(1/5)x

Answer

y = 5x and y = -5x

Answer

y = (1/25)x and y = -(1/25)x

Answer

y = (1/5)x and y = 5x

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Hyperbolas

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Hyperbolas

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