The point on the curve $y^2=x$, where the tangent line makes an angle of $\frac{\pi}{4}$ with x axis is
Answer & explanation
Correct answer: option 3
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