Question

Distance of the normal to the curve $x^2=4y$ which passes through the point $(1,2)$ is

• A. $3$
• B. $\frac{3}{\sqrt{2}}$
• C. $2\sqrt{2}$
• D. $4$

Answer 1

Answer: (B)

Equation of normal to $x^2=4ay$ in standard form is
$x=my-2am-a{m}^3$
$\therefore$ Equation of normal to $x^2=4y$ is
$x=my-2m-m^3$
It passes through the point $(1,2)$
$\therefore 1=2m-2m-m^3$
$\therefore m=-1$
$\therefore$ Equation of normal is $y-2=-(x-1)$
or $x+y-3=0$
Its distance from origin is $\frac{3}{\sqrt{2}}$.