Q. The differential equation $\frac{dy}{dx} = \frac{\sqrt{1 - y^{2}}}{y}$ determines a family of circles with
A) Variable radii and a fixed centre t (0,1)
B) Variable radii and a fixed centre at (0,-1)
C) Fixed radius 1 and variable centres along the x-axis
D) Fixed radius 1 and variable centres along the y-axis
Explanation
(c)
Given, $\frac{dy}{dx} = \frac{\sqrt{1 - y^{2}}}{y}$
$\Rightarrow \$ $\int_{}^{}{\frac{y}{\sqrt{1 - y^{2}}}\ dy} = \int_{}^{}{dx}$
$\Rightarrow$ $- \sqrt{1 - y^{2}} = x + c$
$\Rightarrow$ $(x + c)^{2} + y^{2} = 1$
$\therefore$ Centre ($- c$,0), radius=1
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.