Q139 / 200 · Manipal (MET) 2010 · Mathematics
If the solution of the differential equation $\frac{d y}{d x}=\frac{a x+3}{2 y+f}$ represents a circle, then the value of $a$ is
- A2
- Correct answerB-2
- C3
- D-4
Solution
We have, $\frac{d y}{d x}=\frac{a x+3}{2 y+f}$
$\Rightarrow(a x+3) d x=(2 y+f) d y$
On integrating, we obtain
$a \frac{x^2}{2}+3 x=y^2+f y+c$
$\Rightarrow -\frac{a}{2} x^2+y^2-3 x+f y+c=0$
This will represent a circle, if $-\frac{a}{2}=1$
$\left(\because\right.$ coefficient of $x^2=$ coefficient of $\left.y^2\right)$
$\Rightarrow a=-2$
Hence, the correct answer is option: 'B'.