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.

Simplify the expression.

Raise to the power of .

Apply the product rule to .

Raise to the power of .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Simplify the expression.

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

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

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

Simplify.

The first focus 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 (x^2)/48+(y^2)/64=1