A circle is drawn with center (0,1) and radius 1.
A line OAB is drawn, making an angle θ with the
x-axis to cut the circle at A and the tangent to the
circle at (0,2) at B. Lines are now drawn through
A and B parallel to the x- and y-axes respectively
to intersect at P. Prove that
(i) OA=2 sin θ and
(ii)the coordinates of P are (2 cot θ, 2 sin^2 θ)
Hence, find the Cartesian equation of the locus of P.
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