# How do you find the equation of the hyperbola with center at the origin and foci #(+-10,0)# and asymptotes #y=+-3/4x#?

##### 1 Answer

I am going to use this reference to answer this question.

#### Explanation:

Because the foci are horizontally oriented,

We are told that the center is at the origin, therefore, both h and k equal zero; this makes equation [1] become equation [2]:

The reference tells us that the equations of the asymptotes are,

Matching the above with the given equations,

Which can be written as:

Because the foci are a distance of 10 from the origin, we can write the following equation:

Substitute equation [3] into equation [4] and then solve for "a":

Use equation [3] to compute the value of b:

This makes equation [2] become equation [5]:

Equation [5] is the answer.