Question

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 at (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

Answer 1

Answer: (C)

Fixed radius 1 and variable centres along the x-axis

Answer 2

$\int_{}^{}{\frac{y}{\sqrt{1 - y^{2}}}dy = \int_{}^{}{dx}} \Rightarrow - \sqrt{1 - y^{2}} = (x + c)$]

$\therefore$ x2 + y2 + 2cx + c2 - 1 = 0

Centre (-c, 0) and radius (r) =