Question

If $2x+y+k=0$ is a normal to the parabola $y^2=-8x$, then the value of $k$, is

• A. 8
• B. 16
• C. 24
• D. 32

Answer 1

Answer: (C)

The equation of any normal to the parabola
$y^2=-8x$ is $y=mx+4m+2m^3$ ....(i)
(using equation of normal of parabola in slope form $y=mx-2am-a{m}^3$ and $a=-2)$
But, The given normal is
$2x+y+k=0$
$\Rightarrow y=-2x-k$ ...(ii)
Comparing Eqs. (i) and (ii), we get
$m=-2$
and $-4m-2m^3=k$
$\Rightarrow k=8+16=24$