Question

Let P be a point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, 0 < b < a. Let the line parallel to y-axis passing through P meet the circle x² + y² = a² at the point Q such that P and Q are on the same side of x-axis. For two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s as P varies over the ellipse.

Answer 1

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