The point on the curve $y^2=x$, where the tangent line makes an angle of $\frac{\pi}{4}$ with x axis is

$\left(\frac{1}{4}, \frac{1}{2}\right)$

The correct answer is Option (3) - $\left(\frac{1}{4}, \frac{1}{2}\right)$

$y^2=x$

$2y\frac{dy}{dx}=1⇒\frac{dy}{dx}=\frac{1}{2y}$ when $θ=\frac{\pi}{4}$ with x axis

$\frac{1}{2y}=\tan \frac{\pi}{4}⇒\frac{1}{2y}=1⇒y=\frac{1}{2},x=\frac{1}{4}$

$\left(\frac{1}{4}, \frac{1}{2}\right)$ → point