12.12 Homework: hyperbolas

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

$\frac{y^2}{\left(\frac{1}{4}\right)}-\frac{(x-2{)}^2}{9}=1$

• A

  Is it horizontal or vertical?

• B

  What is the center?

• C

  What is $a$ ?

• D

  What is $b$ ?

• E

  What is $c$ ?

• F

  Graph it. Make sure the box and asymptotes can be clearly seen in your graph.

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

• A

  Put in standard form.

• B

  Is it horizontal or vertical?

• C

  What is the center?

• D

  What is $a$ ?

• E

  What is $b$ ?

• F

  What is $c$ ?

• 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?

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

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.