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Question

Through the vertex O of the parabola y2=4ax two chords OP & OQ are drawn and the circles on OP &OQ as diameter intersect in R. If θ1,θ2 & ϕ are the inclinations of the tangents at P & Q on the parabola and the line through O, R respectively, then the value of cotθ1+cotθ2 is


A
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B
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C
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D
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Solution

The correct option is A
Let P(t1) & Q(t2)
Slope of tangent at P(1t1) & at Q(1t2) cotθ1=t1 and cotθ2=t2
Slope of PQ=2t1+t2=tanϕ
tanϕ=12(cotθ1+cotθ2) cotθ1+cotθ2=2tanθ

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