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