# How do you find all the critical points to graph #9x^2 - 4y^2 - 90x - 32y + 125 = 0# including vertices, foci and asympotes?

##### 1 Answer

The vertices are

The foci are

The equations of the asymptotes are

#### Explanation:

This is the equation of a hyperbola

Rearranging the terms and completing the squares

dividing by

The center of this left right hyperbola is

The vertices are

The slope of the asymptotes are

The equations of the asymptotes are

To calculate the foci, we need

The foci are

graph{(x-5)^2/4-(y+4)^2/9=1 [-13.86, 14.61, -9.24, 5]}