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

The correct option is B $\frac{1}{4}$
Let $y=mx$ is tangent to the parabola $y^2+c=x$

So the equation $m^2{x}^2-x+c=0$ will have equal roots.

$\Rightarrow 1-4c{m}^2=0$

So for perpendicular tangents $m_1{m}_2=-1$

$\Rightarrow \frac{1}{-4c}=-1\Rightarrow c=\frac{1}{4}$