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Find the set of points symmetric to a given point with respect to a circle

by RoRi

We that points P,Q are symmetric with respect to a circle if P and Q are on a line with the center of the circle, the center is not between the points, and the product of their distances from the center is equal to the square of the radius of the circle. Given that Q describes the straight line x + 2y - 5 = 0, find the set of points P symmetric to Q with respect to the circle x^2 + y^2 = 4.

Incomplete.

One comment

  1. S says:

    The idea is that Q=(x_q, (5-x_q)/2), P=t_pQ=16/(5x_q^2+25-10x_q) Q. From that we could get the locus of P, expressed in terms of (x,y), but the concrete numbers get quite messy quite quickly. It is possible that we get a hyperbola.

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