Q. The solution of $\frac{dy}{dx} = \frac{ax + h}{by + k}$ represents a parabola, when
A) $a = 0,\ b = 0$
B) $a = 1,\ b = 2$
C) $a = 0,\ b \neq 0$
D) $a = 2,\ \ b = 1$
Explanation
(c)
Given, $\frac{dy}{dx} = \frac{ax + h}{by + k}$
$\Rightarrow$ $\int_{}^{}{(by + k)}dy = - \int_{}^{}{(ax + h)}\ dx$
$\Rightarrow$ $\frac{by^{2}}{2} + ky = \frac{ax^{2}}{2} + hx + c$
Thus, above equation represents a parabola, if
$a = 0$ and $b \neq o$
Or $b = 0$ and $a \neq 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.