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Parametric Equation of Normal

PQ is a doubl...

Question

PQ is a double ordinate of the parabola $y^{2}$ = 4ax. If the normal at a point P intersects the line passing through Q and parallel to axis of the parabola at G. Then locus of G is a parabola with

Vertex at (4a, 0)

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Equation of directrix is x + 3a = 0

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Length of Latusrectum is 4a

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focus is (4a, 0)

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Solution

The correct options are
A
Vertex at (4a, 0)

C
Length of Latusrectum is 4a

Let P $(a t^{2}, 2 a t) \Rightarrow Q = (a t^{2}, - 2 a t) a n d G = (4 a + a t^{2}, - 2 a t) \begin{matrix} x - 4 a = a t^{2} y = - 2 a t \end{matrix}} \Rightarrow y^{2} = 4 a (x - 4 a)$

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