Question

The line which is parallel to x-axis and crosses the curve $y=\sqrt{x}$ at an angle of $\frac{\pi }{4}$ is

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

Answer 1

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

$y=\sqrt{x}$

$y^{\prime }=\frac{1}{2\sqrt{x}}$

$=tan\theta$
Now $\theta =\frac{\pi }{4}$

$\frac{1}{2\sqrt{x}}=1$

$x=\frac{1}{4}$

$y=\frac{1}{2}$

Now slope of the line is parallel to x axis .

Therefore

$\frac{y-\frac{1}{2}}{x-\frac{1}{4}}=0$

$\Rightarrow y=\frac{1}{2}$.