Question

Let the normal at the point P on the parabola y2 = 6x pass through the point (5, -8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is

• A. -3
• B. $-\frac{9}{4}$
• C. $-\frac{5}{2}$
• D. -2

Answer 1

Answer: (B)

$-\frac{9}{4}$

Answer 2

The correct answer is (B) : $-\frac{9}{4}$
Let P(at2, 2at) where $a=\frac{3}{2}$
T :yt = x + at2 So point Q is
$(−at, at-\frac{a}{t})$
N :y = –tx + 2at + at3 passes through (5, –8)
$−8=−5t+3t+\frac{3}{2}t^3$
⇒ 3t3 – 4t + 16 = 0
⇒ (t + 2)(3t2 – 6t + 8) = 0
⇒ t = –2
So ordinate of point Q is $-\frac{9}{4}$