Question

The differential equation dy/dx = √(1 - y²)/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 is (C) fixed radius 1 and variable centres along the x-axis;

We have

On integrating both sides, we get