The differential equation \(\frac{d y}{d x}=\sqrt{\frac{1-y^{2}}{y}}\) determines a family of circle with
A. variable radii and fixed centre (0, 1)
B. variable radii and fixed centre (0, -1)
C. fixed radius 1 and variable centre on x-axis
D. fixed radius 1 and variable centre on y-axis
Answer:C
The differential equation \(\frac{d y}{d x}=\sqrt{\frac{1-y^{2}}{y}}\) determines a family of circle with
A. variable radii and fixed centre (0, 1) B. variable radii and fixed centre (0, -1) C. fixed radius 1 and variable centre on x-axis D. fixed radius 1 and variable centre on y-axis