Question

The differential equation dy/dx = √((1 – y²)/y) determines a family of circles with

(a) the variable radii and fixed centre at (0, 1) 

(b) the variable radii and fixed centre at (0, –1) 

(c) the fixed radius 1 and variable centre along the x-axis. 

(d) the fixed radius 1 and variable centres along the y-axis.

Answer 1

Answer is (a) The variable radii and fixed centre at (0, 1)

Explanation:

The given differential equation is

Integrating, we get

–√(1 – y²) = x + c

(x + c)² + y² = 1 

which represents a circle with the centre (c, 0) and the radius 1.