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 .

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 .

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 .

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.

Simplify .

Add and .

Add and .

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 an ellipse. Use this form to determine the values used to find the center along with the major and minor axis of the ellipse.

Match the values in this ellipse to those of the standard form. The variable represents the radius of the major axis of the ellipse, represents the radius of the minor axis of the ellipse, represents the x-offset from the origin, and represents the y-offset from the origin.

Find the distance from the center to a focus of the ellipse by using the following formula.

Substitute the values of and in the formula.

Simplify.

Raise to the power of .

Raise to the power of .

Multiply by .

Subtract from .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

The first focus of an ellipse can be found by adding to .

Substitute the known values of , , and into the formula.

The second vertex of an ellipse can be found by subtracting from .

Substitute the known values of , , and into the formula.

Simplify.

Ellipses have two foci.

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Find the Foci 4x^2+16y^2+64x+64y+256=0