To find the area of the ellipse is to find the area of the under the curve. This means that you need to find the definite integral of the function y with respect to x.
First, find the x-intercepts of this equation. The x-intercepts will serve as your bounds.
Then, you will solve for y explicitly from the equation of the ellipse.
Lastly, you will take the integral of y with respect to x. You will evaluate the definite integral using the bounds. The negative x-intercept will be your lower bound. The positive x-intercept will be your upper bound.
As a last step, multiply the result of the definite integral by 2.