If the equation of the normal to the curve x^ | vedclass

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

Question

(D) Given the curve $x^3 - y^2 = 0$.By differentiating with respect to $x$,we get $3x^2 - 2y \frac{dy}{dx} = 0$.So,$\frac{dy}{dx} = \frac{3x^2}{2y}$.A

Vedclass · Accepted Answer

$2/9$

Vedclass · Answer

(D) Given the curve $x^3 - y^2 = 0$.By differentiating with respect to $x$,we get $3x^2 - 2y \frac{dy}{dx} = 0$.So,$\frac{dy}{dx} = \frac{3x^2}{2y}$.At the point $(m^2, -m^3)$,the slope of the tangent is $\left( \frac{dy}{dx} ight)_{(m^2, -m^3)} = \frac{3(m^2)^2}{2(-m^3)} = \frac{3m^4}{-2m^3} = -\frac{3}{2}m$.The slope of the normal is $-\frac{1}{dy/dx} = -\frac{1}{-3m/2} = \frac{2}{3m}$.The equation of the normal at $(m^2, -m^3)$ is $y - (-m^3) = \frac{2}{3m}(x - m^2)$.$y + m^3 = \frac{2}{3m}x - \frac{2m^2}{3m} \Rightarrow y = \frac{2}{3m}x - \frac{2m}{3} - m^3$.Comparing this with the given equation $y = 3mx - 4m^3$,we equate the coefficients of $x$:$3m = \frac{2}{3m} \Rightarrow 9m^2 = 2 \Rightarrow m^2 = \frac{2}{9}$.Also,comparing the constant terms: $-4m^3 = -m^3 - \frac{2m}{3} \Rightarrow 3m^3 = \frac{2m}{3} \Rightarrow 9m^2 = 2 \Rightarrow m^2 = \frac{2}{9}$ (for $m 
eq 0$).

If the equation of the normal to the curve $x^3 - y^2 = 0$ at the point $(m^2, -m^3)$ is $y = 3mx - 4m^3$,then $m^2 = \dots\dots$.

Similar Questions

If the line $ax + by + c = 0$ is a tangent to the curve $xy = 4$,then which of the following is true regarding the signs of $a$ and $b$?

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

The equation of the tangent to the curve $\sqrt{x} + \sqrt{y} = \sqrt{a}$ at the point $(x_1, y_1)$ is:

Find the equation of the line having slope $0$ which is tangent to the curve $y=\frac{1}{x^{2}-2x+3}$.

Let the normal at a point $P$ on the curve $y^{2}-3x^{2}+y+10=0$ intersect the $y$-axis at $(0, \frac{3}{2})$. If $m$ is the slope of the tangent at $P$ to the curve,then $|m|$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module