Question

If the normal at $P\left(18,12\right)$ to the parabola $y^2=8x$ cuts it again at $Q$ , then the equation of the normal at point $Q$ on the parabola $y^2=8x$ is

• A. $27y=99x-3058$
• B. $27y=99x+3058$
• C. $27y=-99x-3058$
• D. None of these

Answer 1

Answer: (A)

Let, $\left(2t^2,4t\right)=\left(18,12\right)$ & $Q=\left(2t_1^2,4t_1\right)$
then $t=3\&t_1=-t-\frac{2}{t}$
$\Rightarrow t_1=-3-\frac{2}{3}=-\frac{11}{3}$
Equation of the normal at $Q$ is
$y=-t_{1}x+4t_1+2t_1^3$
$\Rightarrow y=\frac{11}{3}x-\frac{44}{3}-\frac{2662}{27}$
$\Rightarrow 27y=99x-3058$