Question

If $2x+y+\lambda =0$ is a normal to the parabola $y^2=-8x$, then $\lambda$ is

• A. $12$
• B. $-12$
• C. $24$
• D. $-24$

Answer 1

Answer: (C)

$24$

Given the equation of parabola is
$y^2=-8x$

Here, $a=2$

Equation of normal to parabola having slope $m$ is

$y=mx+2am+a{m}^3$

$y=mx+4m+2m^3$

or $y-mx-4m-2m^3=0$

Given the equation of normal to parabola is

$2x+y+\lambda =0$

On comparing, we get

$m=-2$ and $\lambda =-4m-2m^3$

$\Rightarrow \lambda =8+16=24$