Question

If the solution of the differential equation $\frac{dy}{dx}=\frac{ax+3}{2y+f}$ represents a circle, then the value of ${}^{\prime }{a}^{\prime }$ is

• A. $2$
• B. $-2$
• C. $3$
• D. $-4$

Answer 1

Answer: (B)

We have, $\frac{dy}{dx}=\frac{ax+3}{2y+f}$
$\Rightarrow \left(ax+3\right)dx=\left(2y+f\right)dy$
$\Rightarrow a\frac{x^2}{2}+3x=y^2+fy+C$ (Integrating)
$\Rightarrow -\frac{a}{2}{x}^2+y^2-3x+fy+C=0$
This will represent a circle, if $\frac{-a}{2}=1$
$\Rightarrow a=-2$
$[\because$ coefficient of $x^2=$ coefficient of $y^2]$