Start with two circles centered at the origin with radii 0 < a < b (see figure).

Question:

Start with two circles centered at the origin with radii 0 < a < b (see figure). Assume the line ℓ through the origin intersects the smaller circle at Q and the larger circle at R. Let P(x, y) have the y-coordinate of Q and the x-coordinate of R. Show that the set of points P(x, y) generated in this way for all lines ℓ through the origin is an ellipse.

УА R х