The equation of the straight line which is parallel to $x$-axis and crosses the curve $y=\sqrt{x}$ a

Question

The equation of the straight line which is parallel to $x$-axis and crosses the curve $y=\sqrt{x}$ at an angle of $45^{\circ}$, is

Professor PC Thomas Classes · Answer

Angle with x-axis is $45^{\circ}$, so slope $dy/dx = 	an(45^{\circ}) = 1$. $y = \sqrt{x} \Rightarrow \frac{1}{2\sqrt{x}} = 1 \Rightarrow x = 1/4$. $y = 1/2$.