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  4. PQ is a double ordinate of the parabola y2 = 8x. If the normal at P intersect the line passing through Q and parallel to x-axis at G, then locus of G is a parabola with

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Q. PQ is a double ordinate of the parabola $y^2 = 8x$. If the normal at P intersect the line passing through Q and parallel to x-axis at G, then locus of G is a parabola with

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Solution:

Let $P(at^2 , 2at), Q(at^2 , -2at) $ and $G(h, k)$.
Now, $h = 4a + at^2$ ……(1)
$k = -2at $……(2)
$\therefore $ On eliminating t, we get locus of G
$y ^2 = 4a(x - 4a), $where $a = 2$