The Ellipse - Problem 16

If you have practiced transformations with other types of functions, you will be able to apply them to graphs and equations of conics, as well. Here we begin with ellipses that are not centered at the origin (one in standard form and one presented in general form that we re-write in standard form.) A horizontal shift will go in the parentheses with the x^2 binomial, and a vertical shift will go in the parentheses with the y^2 binomial. Combine like terms inside the parentheses to show the new center. If done correctly, the denominators should not change because we want a rigid translation of the original ellipse shape.