Let P be a point on the ellipse y + -=1, a > b > 0. Let the line...

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Let P be a point on the ellipse y² + -=1, a > b > 0. Let the line parallel to y-axis passing 9² 6² through P meet the circle x² + y² = a² at the point Q such that P and Q are on the same side of the 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 and P varies over the ellipse.

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