Question

If the tangents to the parabola $x=y^2+c$ from origin are perpendicular, then $c$ is equal to

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{1}{4}$
• D. $2$

Answer 1

The correct option is C $\frac{1}{4}$

Parabola : $y^2=x-c$
Tangents from origin are perpendicular
So, origin lies on directrix
Directrix equation for the given curve is
$x=c-\frac{1}{4}$
Origin lies on it, so
$c-\frac{1}{4}=0\therefore c=\frac{1}{4}$