Prove that the locus of the foot of the perpendicular from the focus.of the conic, 1....

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Prove that the locus of the foot of the perpendicular from the focus.of the conic, 1. 1 + e cos 0, on a tangent to it is either a circle or a straight line. Prove that the locus of the foot of the perpendicular from the focus.of the conic, 1. 1 + e cos 0, on a tangent to it is either a circle or a straight line.