# How do you identify the vertices, foci, and direction of #-10y-y^2=-4x^2-72x-199#?

##### 1 Answer

Write the equation in one of the two standard forms then use information to find the vertices and foci.

#### Explanation:

Given:

Add

Remove a common factor of 4 from the first 3 terms and a common factor of -1 from the next 3 terms:

Use the right side of the patterns

Substitute the left side of the patterns into equation [1]:

Substitute the values for h and k into equation [2]:

Simplify the right side of equation [3]:

Divide both sides of the equation by 100:

Write the denominators as squares:

Equation [6] is the standard form for a hyperbola with a horizontal transverse axis.

Referring to the standard form, the vertices are at

Substituting

The vertices are

Referring to the standard form, the foci are at

Use

The foci are

Referring to the standard form, the asymptotes are at:

Substituting

The asymptotes are: