Question

What is the equation of a hyperbola with a=6 and c=9?

Answer 1

`c^2=a^2+b^2` `=>` `9^2=6^2+b^2` `=>` `b^2 = 81-36` `=>` `b^2=45` `=>` `b=+-3sqrt(5)`

`x^2/a^2 - y^2/b^2 = 1` `=>` `x^2/36 - y^2/45 =1`, that is the equation of the hyperbola.