Q. The differential equation of all parabolas whose axes are parallel to y-axis, is
A) $\frac{d^{3}y}{dx^{3}} = 0$
B) $\frac{d^{2}x}{dy^{2}} = c$
C) $\frac{d^{3}y}{dx^{3}} + \frac{d^{2}x}{dy^{2}} = 0$
D) $\frac{d^{2}y}{dx^{2}} + 2\frac{dy}{dx} = c$
Explanation
(a)
The equation of a member of the family of parabolas having axis parallel to $y$-axis is
$y = Ax^{2} + Bx + C$
$\Rightarrow$ $\frac{dy}{dx} = 2Ax + B$
$\Rightarrow$ $\frac{d^{2}y}{dx^{2}} = 2A \Rightarrow \frac{d^{3}y}{dx^{3}} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.