Find the equation of the normal to the curve | vedclass

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

Question

(C) Given line is $2x+18y=9$. The slope of this line is $m = -\frac{2}{18} = -\frac{1}{9}$.Given curve is $y=x^3-3x$. Differentiating with respect to

Vedclass · Accepted Answer

$x+9y=\pm 20$

Vedclass · Answer

(C) Given line is $2x+18y=9$. The slope of this line is $m = -\frac{2}{18} = -\frac{1}{9}$.Given curve is $y=x^3-3x$. Differentiating with respect to $x$,we get $\frac{dy}{dx} = 3x^2-3$.The slope of the normal is $-\frac{1}{\frac{dy}{dx}} = -\frac{1}{3x^2-3}$.Since the normal is parallel to the given line,their slopes are equal:$-\frac{1}{9} = -\frac{1}{3(x^2-1)} \Rightarrow 3(x^2-1) = 9 \Rightarrow x^2-1 = 3 \Rightarrow x^2 = 4 \Rightarrow x = \pm 2$.Case $1$: If $x=2$,then $y = (2)^3 - 3(2) = 8-6 = 2$. The point is $(2, 2)$.The equation of the normal is $y-2 = -\frac{1}{9}(x-2) \Rightarrow 9y-18 = -x+2 \Rightarrow x+9y = 20$.Case $2$: If $x=-2$,then $y = (-2)^3 - 3(-2) = -8+6 = -2$. The point is $(-2, -2)$.The equation of the normal is $y-(-2) = -\frac{1}{9}(x-(-2)) \Rightarrow 9(y+2) = -(x+2) \Rightarrow 9y+18 = -x-2 \Rightarrow x+9y = -20$.Combining both cases,the required equations are $x+9y = \pm 20$.

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

Similar Questions

$P$ is the point of contact of the tangent drawn from the origin to the curve $y = \log_{e} x$. The length of the perpendicular drawn from the origin to the normal at $P$ is

The equation of the normal to the curve $y = \cosh x$ drawn at the point nearest to the origin is

The tangent drawn at the point $(0, 1)$ on the curve $y = e^{2x}$ meets the $x-$axis at the point:

If the normal to the curve $y = f(x)$ at the point $(3, 4)$ makes an angle of $3\pi / 4$ with the positive $X$-axis,find $f'(3)$.

For the curve $xy = c^2$,the subnormal at any point varies as

Vedclass Test Series

Exam Paper Generator

Online Exam Module