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$A line is drawn from A (- 2, 0) to intersect the curve y^{2} = 4 x at P and Q in the first$ $quadrant such that \frac{1}{A P} + \frac{1}{A Q} < \frac{1}{4} . Then the slope of the line is always$

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a

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b

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d

>3

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detailed solution

Correct option is D

Let any point at a distance r from A on the parabola is (-2+rcosθ, rsinθ), P lies on y2=4x ,⇒r2sin2θ =4(-2+rcos θ ), r2sin2θ -4rcosθ+8=0Let P and Q be distances r1 and r2 from A, then r1+r2=4cosθsin2θ, r1r2=8sin2θ1AP+1AQ=1r1+1r2=r1+r2r1r2=cosθ2 Given 1AP+1AQ<14cosθ2<14⇒cosθ<12⇒tanθ>3

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