Let the normal at the point on the parabola y2 = 6x pass through the point (5, -8).

Question

Let the normal at the point 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 :

Accepted Answer

Let P(at2, 2at) where a = $${3 \over 2}$$

T : yt = x + at2 So point Q is $$\left( { - a,\,at - {a \over t}} \right)$$

N : y = -tx + 2at + at3 passes through (5, -8)

-8 = -5t + 3t + $${3 \over 2}$$t3

$$\Rightarrow$$ 3t3 - 4t + 16 = 0

$$\Rightarrow$$ (t + 2) (3t2 - 6t + 8) = 0

$$\Rightarrow$$ t = 2

So ordinate of point Q is - ${9 \over 4}$

Solutions · 1