The equation of the family of curves for whic | vedclass

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

Question

(B) The length of the subnormal at any point $(x, y)$ is given by $|y \frac{dy}{dx}| = k$. This implies $y \frac{dy}{dx} = \pm k$. Separating the vari

Vedclass · Accepted Answer

$y^2 - A = 2Kx$

Vedclass · Answer

(B) The length of the subnormal at any point $(x, y)$ is given by $|y \frac{dy}{dx}| = k$. This implies $y \frac{dy}{dx} = \pm k$. Separating the variables,we get $y \, dy = \pm k \, dx$. Integrating both sides,we obtain $\int y \, dy = \int \pm k \, dx$. This results in $\frac{y^2}{2} = \pm kx + C$,where $C$ is the constant of integration. Multiplying by $2$,we get $y^2 = \pm 2kx + 2C$. Letting $A = 2C$,we have $y^2 - A = \pm 2kx$. Thus,the equation of the family of curves is $y^2 - A = 2Kx$ (considering the positive constant form).

The equation of the family of curves for which the length of the subnormal at any point $(x, y)$ is always a constant $(k)$ is

Similar Questions

The population of a village increases at a rate proportional to the population at that time. In a period of $10$ years,the population grew from $20,000$ to $40,000$. Then,the population after another $20$ years is:

Let $f$ be a non-negative function defined in $[0, \pi / 2]$, $f^{\prime}$ exists and is continuous for all $x$, and $\int_0^x \sqrt{1-\left(f^{\prime}(t)\right)^2} dt = \int_0^x f(t) dt$ with $f(0) = 0$. Then

The $x-$intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve passing through the point $(1, 1)$ is

Radium decomposes at a rate proportional to the amount present. If half the original amount disappears in $1600$ years,then the percentage loss in $100$ years is (Given $\log 2 = 0.6931$ and $e^{-0.0433} = 0.9576$) (in $\%$)

The equation of the family of curves for which the length of the normal is equal to the radius vector is

Vedclass Test Series

Exam Paper Generator

Online Exam Module