First slide

Formation of differential equations

Question

A curve having the condition that the slope of the tangent at some point is two times the slope of the straight lines joining the same point to the origin of co-ordination is a/an

Moderate

A

circle
B

ellipse
C

parabola
D

hyperbola

Solution

$Let p (x, y) be any point on the curve, then \frac{d y}{d x} = 2 \frac{y}{x}$
$\begin{array}{l} \to \int \frac{dy}{y} = 2 \int \frac{dx}{x} \\ \Rightarrow \log y = \log {cx}^{2} \\ \to y = {cx}^{2} is a parabola. \end{array}$

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