Q. The differential equation of all parabolas whose axes are parallel to axis of $x$, is
A) $\frac{d^{3}y}{dx^{3}} = 0$
B) $\frac{d^{3}x}{dy^{3}} = 0$
C) $\frac{d^{2}y}{dx^{2}} + \frac{dy}{dx} = 0$
D) $\frac{d^{2}x}{dy^{2}} = 0$
Explanation
(b)
Equation of parabolas family can be taken as
$x = ay^{2} + by + c$
Differentiating $w.r.t.,\ y$ we get
$\frac{dx}{dy} = 2ay + b$
$\Rightarrow$ $\frac{d^{2}x}{dy^{2}} = 2a\ \ \Rightarrow \frac{d^{3}x}{dy^{3}} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.