Question

If $x+2y=k$ is a normal to $y^2=16x$, then the value of 'k' is

• A. 3
• B. 6
• C. 9
• D. 12

Answer 1

The correct option is C 9

$y=-\frac{1}{2}x+\frac{k}{2}$ is normal to $y^2=16x$
Here $m=-\frac{1}{2}$,
$\therefore$ Using condition of normality,
$c=-2am-a{m}^3$
we get $\frac{k}{2}=-2.4(-\frac{1}{2})-4(-\frac{1}{8})$
$\Rightarrow \frac{k}{2}=\frac{9}{2}\Rightarrow k=9$