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

Question

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 (A) vertex (8, 0) (B) focus (10, 0) (C) directrix as the line x = 6. (D) length of latus rectum equal to 8.

Tardigrade Admin · Accepted Answer

Let P(at2 , 2at), Q(at2 , -2at) and G(h, k). Now, h = 4a + at2 ……(1) k = -2at ……(2) ∴ On eliminating t, we get locus of G y 2 = 4a(x - 4a), where a = 2

Q. PQ is a double ordinate of the parabola $y^{2} = 8 x$ . 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

vertex (8, 0)

focus (10, 0)

directrix as the line x = 6.

length of latus rectum equal to 8.

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

Q. 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