The Ellipse - Problem 17

In the general form of a conic, if the x^2 and y^2 terms are added and have different coefficients and are being added, then you know you have an ellipse. In order to get it into standard form, we need to complete the square on the x's and y's. Lastly, remember that an ellipse equation in standard form needs to be = 1, so if you get anything other than 1 on the right side, you'll need to divide all terms by that value (here, we divide everything by 36.) From standard form, you can identify the coordinates of the center, determine whether its major axis is vertical or horizontal, and length of "a" and "b" in order to sketch the ellipse.