Chapter 12.2, Problem 61E

SKILLS Plus

Ancillary Circle The ancillary circle of an ellipse is the circle with radius equal to half the length of the minor axis and center the same as the ellipse (see the figure). The ancillary circle is thus the largest circle that can fit within an ellipse.

(a) Find an equation for the ancillary circle of the ellipse $x^2+4y^2=16$.

(b) For the ellipse and ancillary circle of part (a), show that if $\left(s,t\right)$ is a point on the ancillary circle, then $\left(2s,t\right)$ is a point on the ellipse.