Practice Hyperbola in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The set of all points in a plane where the absolute difference of the distances to two fixed points (foci) is constant. The curve has two separate branches and asymptotes.

While an ellipse keeps the SUM of distances to foci constant, a hyperbola keeps the DIFFERENCE constant. This creates two separate curves that open away from each other, each curving toward (but never reaching) a pair of asymptotic lines.

Showing a random 20 of 50 problems.

Example 1

hard

Find the equation of a hyperbola with eccentricity

\sqrt{2}

and vertex at

(3, 0)

centered at origin.

Example 2

medium

Convert

4x^2 - 9y^2 = 36

to standard form.

Example 3

easy

Find the center of

\frac{(x+4)^2}{9} - \frac{(y-1)^2}{16} = 1

Example 4

hard

Find the eccentricity of

\frac{x^2}{16} - \frac{y^2}{20} = 1

Example 5

hard

A hyperbola has center at the origin, a vertex at

(0, 6)

, and passes through

(8, 10)

. Find its equation.

Example 6

hard

Identify and convert

4x^2 - y^2 - 16x - 4y + 16 = 0

to standard form.

Example 7

medium

Find the center and foci of

\frac{(x-1)^2}{9}-\frac{(y+2)^2}{16}=1

Example 8

easy

Find the vertices of

\frac{x^2}{36} - \frac{y^2}{49} = 1

Example 9

medium

Find the asymptotes of

9x^2 - 4y^2 = 36

Example 10

challenge

Find the points of intersection between

\frac{x^2}{16} - \frac{y^2}{9} = 1

and the line

y = x

Example 11

challenge

Find the eccentricity of a hyperbola whose asymptotes are

y=\pm x

Example 12

medium

Find the foci of the hyperbola

\frac{x^2}{25} - \frac{y^2}{144} = 1

Example 13

easy

For a hyperbola, the relation between

a

b

, and

c

is ____.

Example 14

easy

Find the vertices of

\frac{x^2}{25}-\frac{y^2}{4}=1

Example 15

hard

Find the equation of the hyperbola with foci

(\pm 10, 0)

and asymptotes

y = \pm \frac{4}{3} x

Example 16

medium

Find the eccentricity of

\frac{x^2}{16}-\frac{y^2}{9}=1

Example 17

medium

Find the foci of

\frac{x^2}{16}-\frac{y^2}{9}=1

Example 18

challenge

Write the equation of a hyperbola with asymptotes

y=\pm\frac{2}{3}x

and a vertex at

(3,0)

Example 19

medium

Find the foci of

\frac{x^2}{9} - \frac{y^2}{40} = 1

Example 20

medium

Find the asymptotes of

\frac{y^2}{16}-\frac{x^2}{9}=1

← Back to Hyperbola Worked Examples Formula Explained

Related Concepts

Equation of a Circle Asymptote Conic Sections Overview