The differential equation $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}$ determines a family of circles with
Answer & explanation
Correct answer: option 3
The given differential equation is
$\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}$
$\Rightarrow \frac{-y}{\sqrt{1-y^2}} d y=-d x$
$\Rightarrow \sqrt{1-y^2}=-x+C$
$\Rightarrow 1-y^2=(x-C)^2 \Rightarrow(x-C)^2+y^2=1$
Clearly, it represents a family of circles of fixed radius 1 and variable centre $(C, 0)$ along the $x$-axis.