Question

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

• A. $x=\frac{1}{4}$
• B. $y=\frac{1}{4}$
• C. $y=\frac{1}{2}$
• D. $y=1$

Answer 1

The correct option is C $y=\frac{1}{2}$

Let the line parallel to x axis be $y=k$.So,the point of intersection of the line and the curve will be $(k^2,k)$ . The slope of the curve at any point $(x,y)$ is $\frac{\partial y}{\partial x}=\frac{1}{2\sqrt{x}}=\frac{1}{2k}=1$
Hence $k=1/2$