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If $P, Q, R$ are three points on a parabola $y^{2} = 4 a x$ whose ordinates are in geometrical progression, then the tangents at $P$ and $R$ meet on

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a

the line through Q parallel to x-axis

b

the line through Q parallel to y-axis

c

the line joining Q to the vertex

d

the line joining Q to the focus.

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detailed solution

Correct option is B

Let the coordinates of P, Q, R be (at2 , 2at ) i =1,2,3 having ordinates in G.P. So that t1, t2, t3 are also in G.P. i.e. t1t3 = t22 . Equations of the tangents at P and R are t1y=x+at12 and t3y=x+at32, which intersect at the point x+at12t1=x+at32t3 ⇒x=at1t3=at22 which is a line through Qparallel to y-axis.

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