Question

What will be the equation of normal to the parabola $y^2=12x$ if the slope of the normal is $2$?

• A. $x+y=18$
• B. $y+36=2x$
• C. $2x-y+36=0$
• D. All of the above.

Answer 1

The correct option is B $y+36=2x$

On comparing parabola $y^2=12x$ with the standard parabola $y^2=4ax$ we get $a=3.$
Also, we have slope of normal $m=2.$
The general slope form equation of normal is $y=mx-2am-a{m}^3.$
On putting the value of slope$m$ and $a=3$ in the equation f normal we get
$y=2x-12-24\Rightarrow y=2x-36.$
Hence the equation of normal is $y=2x-36.$