Question

At what point on the parabola $y^2=4x$ the normal makes equal angles with axes?

• A. $(4,4)$
• B. $(9,6)$
• C. $(4,-4)$
• D. $(1,\pm 2)$

Answer 1

The correct option is D $(1,\pm 2)$

Given equation of parabola is
$y^2=4x$
Here, $a=1$
Let $P(m^2,-2m)$ be any point on the parabola.
Equation of normal having slope $m$ is given by
$y=mx-2am-a{m}^3$
$y=mx-2m-m^3$
Since the normal is equally inclined with axes, so its slope $m=\pm 1$
So, the point $P$ is $(1,\pm 2)$