Question

If the line $y=x+k$ is a normal to the parabola $y^2=4x$ then $k$ can have the value

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

Answer 1

The correct option is C $-3$

Equation of normal to the parabola $y^2=4x$ is given by
$y=mx-2am-a{m}^3..\left(1\right)$, (Here $a=1)$
Now since line (1) and $y=x+k$ represent same line
$\Rightarrow m=1\therefore k=-2am-a{m}^3=-3$