How do you find the equation of the hyperbola with center at the origin and foci #(+-10,0)# and asymptotes #y=+-3/4x#?
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  become equation :
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  into equation  and then solve for "a":
Use equation  to compute the value of b:
This makes equation  become equation :
Equation  is the answer.