# How do you find all the critical points to graph #36x^2 - 100y^2 - 72x + 400y = 3964# including vertices, foci and asymptotes?

##### 1 Answer

Vertices are

#### Explanation:

The graph is for a hyperbola.

The standard form of equation for a hyperbola is

What we have to do is to deform the fomula to this form.

[step1] Let's complete the square.

[step2] divide both side by

The hyperbola has vertices and foci on on the line

Substituting

Therefore, the vertices are

The foci of

If the fomula were

(

The asymptopes of