Question

Find the point on the curve $y^2=x,$ at which the tangent makes an angle of ${45}^{\circ }$ with $x-$axis.

• A. $(\frac{1}{4},\frac{1}{2})$
• B. $(\frac{1}{4},1)$
• C. $(\frac{1}{8},\frac{1}{2})$
• D. $(1,\frac{1}{2})$

Answer 1

The correct option is A $(\frac{1}{4},\frac{1}{2})$

Here $m=\tan {45}^{\circ }=1$ and $a=\frac{1}{4}$
point is $(\frac{a}{m^2},\frac{2a}{m})$ or $(\frac{1}{4},\frac{1}{2})$
Ans: A