Question

A parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola

• A. y2 = 16x
• B. y2 = 4x
• C. y2 = 8x
• D. x2 = 4y

Answer 1

Answer: (A)

y2 = 16x

Answer 2

Given parabola y2 = 12x

$\frac{t_1}{t_2}=3=t_1=3t_2....(i)$

Let point of intersection be (h, k)

$h=3t_1t_2 ....(ii)$

$and \,\,k=3(t_1+t_2)........(iii)$

$\frac{k}{12}$….(i)

$$$9×\frac{k^2}{144}$

The correct option is (A): y2 = 16x