# Graph nine i plus twelve j

Shift and .

Find the standard form of the hyperbola.

Subtract from both sides of the equation.

First, divide each term by to make the right side equal to one.

Clarify each term in the equation in order to set the right side equal to . The right side of the equation must equal for an ellipse or hyperbola to have the standard form.

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

Compare the values in this hyperbola to those of the initial 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 left and right.

Clarify .

Add and .

Add and .

Simplify .

Add and .

Combine and .

This hyperbola has two asymptotes.

The asymptotes are and .

Asymptotes:

Asymptotes:

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