The differential equation `(dy)/(dx)=(sqrt(1-y^2))/y` determines a family of circle with

Options

A. variables 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

b

Explanation

Given , `(dy)/(dx) = (sqrt(1-y^(2))/y)`
` rArr int y/(sqrt(1-y^(2))) dy = int dx `
` rArr - sqrt (1-y^(2))= x+C`
` rArr (x + C)^(2) + y^(2) = 1 `
` :. " Centre (-C,0), radius "=1`