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find locus with angle condition

Source: LIMIT 2019 CBS2 P4

April 28, 2021
geometry

Problem Statement

A particle PP moves in the plane in such a way that the angle between the two tangents drawn from PP to the curve y2=4axy^2=4ax is always 90∘90^\circ. The locus of PP is <spanclass=′latex−bold′>(A)</span> a parabola<span class='latex-bold'>(A)</span>~\text{a parabola} <spanclass=′latex−bold′>(B)</span> a circle<span class='latex-bold'>(B)</span>~\text{a circle} <spanclass=′latex−bold′>(C)</span> an ellipse<span class='latex-bold'>(C)</span>~\text{an ellipse} <spanclass=′latex−bold′>(D)</span> a straight line<span class='latex-bold'>(D)</span>~\text{a straight line}
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