ParabolaHard

Question

Let PQ be a double ordinate of the parabola, y2 = − 4x, where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1 then the locus of R is :

Options

A.3y2 = − 2x
B.3y2 = 2x
C.9y2 = 4x
D.9y2 = − 4x

Solution

Let P (-at12 2at1), Q(-at12, - 2at1), R(h, k)
⇒ h = - at12, k =
⇒ 9k2 = - 4h ⇒ 9y2 = - 4x

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