Grade 12 Hyperbola Worksheet
This worksheet covers key concepts of hyperbolas, including their standard equations, foci, vertices, asymptotes, and graphing.
Includes
Standards
Topics
Hyperbolas: Properties and Graphing
Name:
Date:
Score:
Read each question carefully and provide detailed answers. Show all your work for full credit.
1. Which of the following is the standard form equation of a hyperbola centered at the origin with a horizontal transverse axis?
x²/a² + y²/b² = 1
x²/a² - y²/b² = 1
y²/a² - x²/b² = 1
y²/a² + x²/b² = 1
2. The distance from the center to each focus of a hyperbola is denoted by:
a
b
c
e
1. The two separate curves of a hyperbola are called its .
2. The line segment connecting the two vertices of a hyperbola is called the axis.
3. The equations of the asymptotes for a hyperbola centered at the origin with a horizontal transverse axis are y = ±( / )x.
1. Find the vertices, foci, and asymptotes of the hyperbola with the equation x²/16 - y²/9 = 1. Then, sketch its graph.
2. Write the standard form equation of a hyperbola with vertices at (0, ±5) and foci at (0, ±8).
1. The eccentricity of a hyperbola is always greater than 1.
True
False
2. The conjugate axis of a hyperbola is perpendicular to its transverse axis.
True
False
Match each term with its correct definition.
1. Transverse Axis
a. The line segment perpendicular to the transverse axis, passing through the center.
2. Conjugate Axis
b. The two points on the hyperbola that are closest to the center.
3. Vertices
c. The line segment connecting the two vertices of a hyperbola.
4. Foci
d. The two fixed points used to define a hyperbola.