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 eccentricity by using the following formula.

Substitute the values of and into the formula.

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 result can be shown in multiple forms.

Exact Form:

Decimal Form:

Find the Eccentricity ((y+5)^2)/169+((x-3)^2)/49=1