Question

The normal at an end of a latus rectum of the parabola $y^2=36x$ meets the parabola again at the point

• A. $(81,-54)$
• B. $(81,54)$
• C. $(9,18)$
• D. $(9,-18)$

Answer 1

Answer: (A), (B)

The correct options are
A $(81,-54)$
B $(81,54)$

Given equation of the parabola is $y^2=36x$
Focus $S=(9,0)$
Ends of latusrectum are $(9,18)$ and $(9,-18)$ whose parametric values are $t=1$ and $t=-1$ respectively.
Let the normal drawn at $P(9,18)$ meets the parabola again at $Q$.
If normal drawn at $t_1$ meets the parabola again at $t_2$ then $t_2=-t_1-\frac{2}{t_1}$
$\Rightarrow t_2=-1-2=-3$
$\therefore Q$ is $(81,-54)$
Let the normal drawn at $R(9,-18)$ meets the parabola again at $S$.
$\Rightarrow t_2=1+2=3$
$\therefore S$ is $(81,54)$
Hence, options A and B.