Ellipses for Curves

You can use an interactive ellipses to approximate curves. If you use a parent function of an ellipse as shown at the bottom left and have the coordinates (h,k+b) and (h+a,k) you can make a scalable ellipse that you can drag to match curves. You can also plot (h,k) as the center of the ellipse and use it to move the ellipse without changing the sides. Make sure the (h,k+b) can only move vertically and the (h+a,k) can only move horizontally by clicking into the circle to the left of the equation to ensure that the ellipse transforms properly. Once you have the ellipse matching the curve you can take your h,k,a, and b values and plug them into the ellipse equation (x-h)^2/a^2 + (y-k)^2/b^2=1 on a separate line to make an ellipse that you can easily shape. If you don't want the full ellipse you can add limits to the ellipse to include only the section that you want.