A hyperbola centered at (0,0)

Name: Carla
Level of Question: Secondary (12)
Asking question: Student

Find the equation of the hyperbola centered at (0,0) with vertices at (0,3) and (0,-3) that is asymptotic to the lines y=+-5x.
Find the equation of a hyperbola in standard position foci (1,5) and (1,7) and eccentricity 2.

Thank you for your help and effort. Have a nice holiday and New Year!!! Thanks again!!!

Hi Carla,

For problem 1 the center being (0,0) and the vertices on the y-axis means that the hyperbola has the form

In this equation when x = 0, y² = b², that is y = +-b. But you know that (0,3) and (0,-3) are on the graph and hence b = 3.

I remember that to find the asymptotes of the hyperbola in standard form you factor the left side as a difference of squares.

The two asymptotes are then

and

This should allow you to find a.