The point on the curve y² = x, the tangent at which makes an angle of 45° with x-axis will be given by

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

$y^2=x \Rightarrow 2 y \frac{d y}{d x}=1$

$\Rightarrow \frac{d y}{d x}=\frac{1}{2 y}=\tan 45°=1$  (given)

$\Rightarrow y=\frac{1}{2}$      ∴  $x=\frac{1}{4}$

∴  Point is $\left(\frac{1}{4}, \frac{1}{2}\right)$.