Grade 11 · Math · Algebra 2

11th grade Hyperbolas: parts, equations and graphs worksheet

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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 parabola
- an ellipse
- a hyperbola
- a circle
2.
Zee writes a curve on graph paper as 16x² + 25y² + 64x − 50y − 311 = 0. Which kind of curve is it?
- a hyperbola
- a parabola
- a circle
- an ellipse
3.
Esme writes a hyperbola on graph paper as 4x² − 9y² − 8x + 36y − 176 = 0. Which equation is the same curve in standard form?
- (x − 1)²/4 − (y − 2)²/9 = 1
- (x + 1)²/36 − (y + 2)²/16 = 1
- (x − 1)²/36 − (y − 2)²/16 = 1
- (x − 1)²/16 − (y − 2)²/36 = 1
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?
- (y − 1)²/16 − (x + 3)²/36 = 1
- (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
6.
Milo writes a hyperbola on graph paper as 9x² − 4y² + 18x − 16y + 137 = 0. Which equation is the same curve in standard form?
- (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
- (x + 1)²/16 − (y + 2)²/36 = 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 = ±(49/16)(x − 3)
- y + 2 = ±(7/4)(x − 3)
- y + 2 = ±(4/7)(x − 3)
- y − 2 = ±(7/4)(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 = ±(6/5)(x + 3)
- y − 1 = ±(36/25)(x + 3)
- y + 1 = ±(6/5)(x − 3)
- y − 1 = ±(5/6)(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 = ±(8/3)(x + 1)
- y − 4 = ±(9/64)(x + 1)
- y − 4 = ±(3/8)(x + 1)
- y + 4 = ±(3/8)(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 = ±(81/4)(x − 5)
- y + 2 = ±(2/9)(x − 5)
- y − 2 = ±(9/2)(x + 5)
- y + 2 = ±(9/2)(x − 5)

11th grade Hyperbolas: parts, equations and graphs worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Hyperbolas: parts, equations and graphs. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the center, vertices and foci of a hyperbola, with c² = a² + b², and tell which way it opens.
I can find the asymptotes as the diagonals of the box a across and b up.
I can complete both squares to write a hyperbola in standard form, and tell an ellipse from a hyperbola by the signs.

Standard: G-GPE.A.3 (+)

Words to know

hyperbola: Every point whose two distances to the foci differ by the same number.

branches: The two separate curves of a hyperbola.

vertices: The two points where the branches turn, a from the center.

foci: The two marked points inside the branches, c from the center.

asymptotes: Two lines the branches get closer and closer to.

plus term: The squared term with the plus sign; it tells which way the curve opens.

Common mistakes

Your child added the two distances, which is the rule for an ellipse.

Your child gave one of the two distances instead of their difference.

Your child added the steps across and up instead of finding the slanted distance.

What to say

Ask: on a hyperbola, are the distances added or subtracted?

Ask: how far is the point from the other focus?

Ask: is the slanted path shorter than the two steps together?

Questions parents ask

What is the most common mistake with hyperbolas: parts, equations and graphs?

Your child added the two distances, which is the rule for an ellipse.

How can I help my child with hyperbolas: parts, equations and graphs?

Ask: on a hyperbola, are the distances added or subtracted?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

See all Algebra 2

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