Question

The point on the curve $y^2=x$ where the tangent makes an angle of $\frac{\pi }{4}$ with X - axis is

• A. (4, 2)
• B. $(\frac{1}{4},\frac{1}{2})$
• C. (1, 1)
• D. $(\frac{1}{2},\frac{1}{4})$

Answer 1

Answer: (B)

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

$y^2=x$
Differentiatie both sides w.r.t. x
$2y\frac{dy}{dx}=1$
$\frac{dy}{dx}=\frac{1}{2y}$
Also, tangent makes an angle of $\frac{\pi }{4}$ with x axis
$\frac{dy}{dx}=\tan \frac{\pi }{4}$
$=1$
$\therefore \frac{1}{2y}=1$
$y=\frac{1}{2}$
Put value of y in equation $y^2=x$
$x=\frac{1}{4}$
Point $(\frac{1}{4},\frac{1}{2})$