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Question

The portion of the tangent intercepted between the point of contact and the directrix of the parabola \( y^2 = 4ax\) subtends at the focus an angle of

A
30
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B
45
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C
60
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D
90
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Solution

The correct option is D 90
If P=(at2,2at) then the equation of tangent at t is ty=x+at2 .......(1)
Directrix is x+a=0............(2)
By solving Q=[a,a(t21)t],S=(a,0)
Slope of SP=2ata(t21)=2tt21,Slope of SQ=a(t21)t2a=(t21)2t
Product of slopes = –1. PSQ=90

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