# How do you find all the critical points to graph #4x^2 + 20x - 4y^2 + 6y - 3 = 0# including vertices, foci and asymptotes?

##### 1 Answer

Oct 18, 2016

The graph is a hyperbola and we have to write the equation in the standard form.

So the equation becomes

So the center is

The vertices are

The slope of the asymptotes are 1 and -1

The equations of the asymptotes are

In order to determine the foci we need

So the foci are

graph{4*x^2+20*x-4*y^2+6*y-3=0 [-20, 20, -10, 10]}