How do you find the standard form of the equation of the hyperbola given the properties foci #(+-5,0)#, length of the conjugate axis 6?
Please see the explanation.
Because the foci are given to be
We know that
Substitute the value for "b" into equation :
We know that the general forms for the foci are:
This allows us to write the following equations:
Substitute the value for k into equation :
Find the value of h by adding equations  and :
Substitute into equation :
Use equation  to find the value of "a":
#25 = a^2+9
Substitute the value of "a" into equation 
Equation  is the equation of the hyperbola.