Question

The normal to the parabola $y^2=8x$ at $(2,4)$ meets the parabola again at

• A. $(18,12)$
• B. $(18,-12)$
• C. $(-18,12)$
• D. None of these

Answer 1

The correct option is B $(18,-12)$

$=>y^2=8x.............\left(i\right)(a=2)$

Normal is drawn at $(2,4)$

Let the parametric point be $({at}^2,2at)=>({2t}^2,4t)$

And the normal at $T$ meets again $\left(i\right)$ at $t_2=t-\frac{2}{t}$

Now ${2t}^2=2and4t=4$

$=>t=1$

Now, $t_2=-1-2=-3$

The point at which normal meets parabola again is $(a{t}^2,2a{t}_2):({2t}^2,4t)$

$:(18,-12)$.