Hyperbolas: parts, equations and graphs

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer.

1.
Ren writes a curve on graph paper as 9x² + 4y² − 18x + 16y − 11 = 0. Which kind of curve is it?
- a circle
- an ellipse
- a hyperbola
- a parabola
2.
Tala writes a curve for a lamp's light on a wall as -4x² + 25y² + 8x + 50y − 79 = 0. Which kind of curve is it?
- a parabola
- a hyperbola
- a circle
- an ellipse
3.
Zee writes a curve on graph paper as 16x² + 25y² + 64x − 50y − 311 = 0. Which kind of curve is it?
- a hyperbola
- a circle
- a parabola
- an ellipse
4.
Jun writes a hyperbola on a map as 9x² − 4y² + 36x + 8y − 112 = 0. Which equation is the same curve in standard form?
- (x + 2)²/16 − (y − 1)²/36 = 1
- (x − 2)²/16 − (y + 1)²/36 = 1
- (x + 2)²/9 − (y − 1)²/4 = 1
- (x + 2)²/36 − (y − 1)²/16 = 1
5.
Luz writes a lamp's light on a wall as 4x² − 9y² − 24x − 18y + 171 = 0. Which equation is the same curve in standard form?
- (x − 3)²/36 − (y + 1)²/16 = 1
- (y + 1)²/9 − (x − 3)²/4 = 1
- (y + 1)²/16 − (x − 3)²/36 = 1
- (y − 1)²/16 − (x + 3)²/36 = 1
6.
Milo writes a hyperbola on graph paper as 9x² − 4y² + 18x − 16y + 137 = 0. Which equation is the same curve in standard form?
- (x + 1)²/16 − (y + 2)²/36 = 1
- (y + 2)²/4 − (x + 1)²/9 = 1
- (y − 2)²/36 − (x − 1)²/16 = 1
- (y + 2)²/36 − (x + 1)²/16 = 1
7.
Noah draws a hyperbola on a map as (x − 3)²/16 − (y + 2)²/49 = 1. Which lines are its asymptotes?
- y + 2 = ±(7/4)(x − 3)
- y − 2 = ±(7/4)(x + 3)
- y + 2 = ±(4/7)(x − 3)
- y + 2 = ±(49/16)(x − 3)
8.
Ren traces a lamp's light on a wall as (y − 1)²/36 − (x + 3)²/25 = 1. Which lines are its asymptotes?
- y − 1 = ±(36/25)(x + 3)
- y + 1 = ±(6/5)(x − 3)
- y − 1 = ±(5/6)(x + 3)
- y − 1 = ±(6/5)(x + 3)
9.
Tala draws the hyperbola (x + 1)²/64 − (y − 4)²/9 = 1 on graph paper. Which lines are its asymptotes?
- y − 4 = ±(3/8)(x + 1)
- y + 4 = ±(3/8)(x − 1)
- y − 4 = ±(9/64)(x + 1)
- y − 4 = ±(8/3)(x + 1)
10.
Zee draws the hyperbola (y + 2)²/81 − (x − 5)²/4 = 1 on graph paper. Which lines are its asymptotes?
- y − 2 = ±(9/2)(x + 5)
- y + 2 = ±(2/9)(x − 5)
- y + 2 = ±(81/4)(x − 5)
- y + 2 = ±(9/2)(x − 5)

Hyperbolas: parts, equations and graphs

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer.

1.
Ren writes a curve on graph paper as 9x² + 4y² − 18x + 16y − 11 = 0. Which kind of curve is it?
- a circle
- an ellipse
- a hyperbola
- a parabola
2.
Tala writes a curve for a lamp's light on a wall as -4x² + 25y² + 8x + 50y − 79 = 0. Which kind of curve is it?
- a parabola
- a hyperbola
- a circle
- an ellipse
3.
Zee writes a curve on graph paper as 16x² + 25y² + 64x − 50y − 311 = 0. Which kind of curve is it?
- a hyperbola
- a circle
- a parabola
- an ellipse
4.
Jun writes a hyperbola on a map as 9x² − 4y² + 36x + 8y − 112 = 0. Which equation is the same curve in standard form?
- (x + 2)²/16 − (y − 1)²/36 = 1
- (x − 2)²/16 − (y + 1)²/36 = 1
- (x + 2)²/9 − (y − 1)²/4 = 1
- (x + 2)²/36 − (y − 1)²/16 = 1
5.
Luz writes a lamp's light on a wall as 4x² − 9y² − 24x − 18y + 171 = 0. Which equation is the same curve in standard form?
- (x − 3)²/36 − (y + 1)²/16 = 1
- (y + 1)²/9 − (x − 3)²/4 = 1
- (y + 1)²/16 − (x − 3)²/36 = 1
- (y − 1)²/16 − (x + 3)²/36 = 1
6.
Milo writes a hyperbola on graph paper as 9x² − 4y² + 18x − 16y + 137 = 0. Which equation is the same curve in standard form?
- (x + 1)²/16 − (y + 2)²/36 = 1
- (y + 2)²/4 − (x + 1)²/9 = 1
- (y − 2)²/36 − (x − 1)²/16 = 1
- (y + 2)²/36 − (x + 1)²/16 = 1
7.
Noah draws a hyperbola on a map as (x − 3)²/16 − (y + 2)²/49 = 1. Which lines are its asymptotes?
- y + 2 = ±(7/4)(x − 3)
- y − 2 = ±(7/4)(x + 3)
- y + 2 = ±(4/7)(x − 3)
- y + 2 = ±(49/16)(x − 3)
8.
Ren traces a lamp's light on a wall as (y − 1)²/36 − (x + 3)²/25 = 1. Which lines are its asymptotes?
- y − 1 = ±(36/25)(x + 3)
- y + 1 = ±(6/5)(x − 3)
- y − 1 = ±(5/6)(x + 3)
- y − 1 = ±(6/5)(x + 3)
9.
Tala draws the hyperbola (x + 1)²/64 − (y − 4)²/9 = 1 on graph paper. Which lines are its asymptotes?
- y − 4 = ±(3/8)(x + 1)
- y + 4 = ±(3/8)(x − 1)
- y − 4 = ±(9/64)(x + 1)
- y − 4 = ±(8/3)(x + 1)
10.
Zee draws the hyperbola (y + 2)²/81 − (x − 5)²/4 = 1 on graph paper. Which lines are its asymptotes?
- y − 2 = ±(9/2)(x + 5)
- y + 2 = ±(2/9)(x − 5)
- y + 2 = ±(81/4)(x − 5)
- y + 2 = ±(9/2)(x − 5)