The length of the subtangent at any point of | vedclass

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

Question

(B) Given the curve equation: $x^m y^n = a^{m+n}$.Taking the natural logarithm on both sides: $m \ln x + n \ln y = \ln(a^{m+n})$.Differentiating with

Vedclass · Accepted Answer

Abscissa

Vedclass · Answer

(B) Given the curve equation: $x^m y^n = a^{m+n}$.Taking the natural logarithm on both sides: $m \ln x + n \ln y = \ln(a^{m+n})$.Differentiating with respect to $x$: $\frac{m}{x} + \frac{n}{y} \frac{dy}{dx} = 0$.Thus,$\frac{dy}{dx} = -\frac{m}{n} \frac{y}{x}$.The length of the subtangent is given by the formula: $LST = \left| \frac{y}{dy/dx} \right|$.Substituting the value of $\frac{dy}{dx}$: $LST = \left| \frac{y}{(-\frac{m}{n} \frac{y}{x})} \right| = \left| -\frac{nx}{m} \right| = \frac{n}{m} |x|$.Since $\frac{n}{m}$ is a constant,the length of the subtangent is proportional to the abscissa $x$.

The length of the subtangent at any point of the curve $x^my^n = a^{m+n}$ is proportional to

Similar Questions

If the lines $x+y=a$ and $x-y=b$ touch the curve $y = x^{2}-3x+2$ at the points where the curve intersects the $x$-axis,then $\frac{a}{b}$ is equal to:

If the tangent to the curve $y = \frac{x}{x^2-3}$,$x \in R, (x \neq \pm \sqrt{3})$ at a point $(\alpha, \beta) \neq (0,0)$ on it,is parallel to the line $2x + 6y - 11 = 0$,then

If the length of the subnormal is equal to the length of the subtangent at any point on the curve $y = f(x)$ and the tangent at $(3, 4)$ to $y = f(x)$ meets the positive coordinate axes at $A$ and $B$,then the area of $\Delta OAB$,where $O$ is the origin,is

The equation of the normal to the curve $y^4=a x^3$ at $(a, a)$ is

The length of the normal to the curve $x = a(\theta + \sin \theta)$,$y = a(1 - \cos \theta)$ at the point $\theta = \pi/2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module