Question

The line which is parallel to X-axis and crosses the curve $y = \sqrt{x}$ at an 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

Answer: (C)

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