Question

The differential equation representing the family of parabolas having vertex at origin and axis along positive direction of $x-axis$ is

• A. $y^2-2xy\frac{dy}{dx}=0$
• B. $y^2+2xy\frac{dy}{dx}=0$
• C. $y^2-2xy\frac{d^{2}y}{d{x}^2}=0$
• D. $y^2+2xy\frac{d^{2}y}{d{x}^2}=0$

Answer 1

Answer: (A)

The equation of family of parabola having vertex at origin and axis along positive direction of axis of $x$ is given as
$y^2=4ax\dots (i)$
$\Rightarrow 2y\frac{dy}{dx}=4a$
$\Rightarrow 2y\frac{dy}{dx}$
$=\frac{y^2}{x}$ [using Eq. (i)]
$\Rightarrow \frac{y^2}{x}-2y\frac{dy}{dx}=0$
$\Rightarrow y^2-2xy\frac{dy}{dx}=0$