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Homework: Hyperbolas

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides homework problems related to hyperbolas.

Exercise 1

Complete the following chart, showing the similarities and differences between ellipses and hyperbolas.

Table 1
  Ellipse Hyperbola
How to identify an equation with this shape Has an x 2 x 2 and a y 2 y 2 with different coefficients but the same sign. 3 x 2 + 2 y 2 3 x 2 +2 y 2 for instance.  
Equation in standard form: horizontal ( x−h )2 a2 ( y−k )2 b2 = 1 ( x−h )2 a2 ( y−k )2 b2 =1  
How can you tell if it is horizontal?    
Draw the shape here. Label a a, b b, and c c on the drawing.    
Center ( h h, k k)  
What a a represents on the graph    
What b b represents on the graph    
What c c represents on the graph    
Which is the biggest, a a, b b, or c c?    
Mathematical relationship between a a, b b, and c c.    

Exercise 2

y 2 ( 1 4 ) - ( x - 2 ) 2 9 = 1 y 2 ( 1 4 ) - ( x - 2 ) 2 9 =1

  • a. Is it horizontal or vertical?
  • b. What is the center?
  • c. What is aa?
  • d. What is bb?
  • e. What is cc?
  • f. Graph it. Make sure the box and asymptotes can be clearly seen in your graph.

Exercise 3

2 x 2 + 8 x - 4 y 2 + 4 y = 6 2 x 2 +8x-4 y 2 +4y=6

  • a. Put in standard form.
  • b. Is it horizontal or vertical?
  • c. What is the center?
  • d. What is aa?
  • e. What is bb?
  • f. What is cc?
  • g. Graph it. Make sure the box and asymptotes can be clearly seen in your graph.
  • h. What is the equation for one of the asymptotes that you drew?

Exercise 4

A hyperbola has vertices at the origin and (10,0). One focus is at (12,0). Find the equation for the hyperbola.

Exercise 5

A hyperbola has vertices at (1,2) and (1,22), and goes through the origin.

  • a. Find the equation for the hyperbola.
  • b. Find the coordinates of the two foci.

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