Question

The normal at P(18, 12) to the parabola y²= 8x cut it again at Q, then the length of PQ is

• A. $\frac{8\sqrt{10}}{9}$
• B. $\frac{9\sqrt{10}}{8}$
• C. $\frac{90\sqrt{10}}{9}$
• D. $\frac{80\sqrt{10}}{9}$

Answer 1

Answer: (D)

$\frac{80\sqrt{10}}{9}$

Answer 2

P(18, 12) = ($at_{1}^{2},\mspace{6mu} 2at_{1})$

⇒ t₁ = 3

We know that the length of normal chord drawn at t

= $\frac{4a(1 + t^{2})^{3/2}}{t^{2}} = \frac{80\sqrt{10}}{9}$