The points on the curve y^2 = x + sin x at wh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given curve is $y^2 = x + \sin x$ ...$(i)$By differentiating with respect to $x$,we get $2y \frac{dy}{dx} = 1 + \cos x$,which implies $\frac{dy}{d

Vedclass · Accepted Answer

a parabola

Vedclass · Answer

(C) Given curve is $y^2 = x + \sin x$ ...$(i)$By differentiating with respect to $x$,we get $2y \frac{dy}{dx} = 1 + \cos x$,which implies $\frac{dy}{dx} = \frac{1 + \cos x}{2y}$.The slope of the normal is $m = -\frac{1}{dy/dx} = -\frac{2y}{1 + \cos x}$.For the normal to be parallel to the $Y$-axis,the slope must be undefined,i.e.,$1 + \cos x = 0$.This implies $\cos x = -1$,which means $x = (2n+1)\pi$ for some integer $n$.At these points,$\sin x = 0$.Substituting $\sin x = 0$ into the original equation $(i)$,we get $y^2 = x + 0$,or $y^2 = x$.This is the equation of a parabola.

The points on the curve $y^2 = x + \sin x$ at which the normal is parallel to the $Y$-axis lie on

Similar Questions

Find the equation of the normal to the curve $y=x^3-3x$ which is parallel to the line $2x+18y=9$.

The angle between the curves $y=\sin 2x$ and $y=\cos 2x$ is

The tangent to a given curve $y=f(x)$ is perpendicular to the $x$-axis,if

The coordinates of the point on the curve $9y^2 = x^3$ where the normal to the curve makes equal intercepts with the axes are:

For the curve $b{y^2} = {(x + a)^3}$,the square of the subtangent is proportional to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module