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, $\left(2 t^{2} , 4 t\right)=\left(18,12\right)$ & $Q=\left(2 t_{1}^{2} , 4 t_{1}\right)$
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
$y=-t_{1}x+4t_{1}+2t_{1}^{3}$
$\Rightarrow y=\frac{11}{3}x-\frac{44}{3}-\frac{2662}{27}$
$\Rightarrow 27y=99x-3058$