# Find the Asymptotes 81x^2-y^2-810x-10y+2009=0

Find the standard form of the hyperbola.
Subtract from both sides of the equation.
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Subtract from .
Substitute the values of , , and into the vertex form .
Substitute for in the equation .
Move to the right side of the equation by adding to both sides.
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Move the negative one from the denominator of .
Multiply.
Multiply by .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Substitute the values of , , and into the vertex form .
Substitute for in the equation .
Move to the right side of the equation by adding to both sides.
Simplify .
Subtract from .
Flip the sign on each term of the equation so the term on the right side is positive.
Divide each term by to make the right side equal to one.
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.
Simplify to find the first asymptote.
Remove parentheses.
Simplify .
Simplify each term.
Multiply by .
Apply the distributive property.
Multiply by .
Subtract from .
Simplify to find the second asymptote.
Remove parentheses.
Simplify .
Simplify each term.
Multiply by .
Apply the distributive property.
Multiply by .
Subtract from .
This hyperbola has two asymptotes.
The asymptotes are and .
Asymptotes:
Find the Asymptotes 81x^2-y^2-810x-10y+2009=0