First slide

Applications of differential equations

Question

A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates is

Moderate

A

a circle
B

an ellipse
C

a parabola
D

a hyperbola

Solution

Since, slope of line joining to point P(x, y) and origin is y/x
Slope of tangent at P is $\frac{dy}{dx}$
It is given that,
$\begin{array}{l} \frac{dy}{dx} = \frac{2 y}{x} \\ \Rightarrow \frac{dy}{y} = 2 \frac{dx}{x} \\ \Rightarrow \int \frac{dy}{y} = 2 \int \frac{dx}{x} \\ \Rightarrow \log y = 2 \log x + \log C \\ \Rightarrow y = x^{2} C \end{array}$
which represents the equation of a parabola.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App