Question

The point on the curve $y^2=x$ where tangent makes ${45}^o$ angle with $x-$axis ?

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

Answer 1

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

$\frac{dy}{dx}=$ Slope of the tangent at that point of the curve.

Given curve is $x=y^2$

Keep $y=a,thenx=y^2$

point $(a^2,a)$

$\frac{dy}{dx}(y^2-x)=0\frac{dy}{dx}=\frac{1}{2y}=\frac{1}{2a}=\tan \left({45}^0\right)$

$\Rightarrow a=\frac{1}{2}{a}^2=\frac{1}{4}$

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