Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .

This is the form of a hyperbola. Use this form to determine the values used to find the asymptotes of the hyperbola.

Match the values in this hyperbola to those of the standard form. The variable represents the x-offset from the origin, represents the y-offset from origin, .

The asymptotes follow the form because this hyperbola opens up and down.

Remove parentheses.

Simplify .

Simplify each term.

Multiply by .

Apply the distributive property.

Combine and .

Multiply .

Combine and .

Multiply by .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Remove parentheses.

Simplify .

Simplify each term.

Multiply by .

Apply the distributive property.

Combine and .

Multiply .

Multiply by .

Combine and .

Multiply by .

Move to the left of .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

This hyperbola has two asymptotes.

The asymptotes are and .

Asymptotes:

Find the Asymptotes ((y+8)^2)/121-((x-3)^2)/25=1