The differential equation `(dy)/(dx)=(sqrt(1-y^2))/y` determines a family of circle with (a) variable radii and a fixed centre at (0, 1) (b) variable radii and a fixed centre at `( c ) (d)(( e ) (f)0,-1( g ))( h )` (i) (j) Fixed radius 1 and variable centres along the x-axis. (k) Fixed radius 1 and variable centres along the y-axis.

Options

A. (a) variable radii and a fixed centre at (0,1)
B. (b) variavle radii and a fixed centre at (0,-1)
C. (c) fixed radius 1 and variable centres along the X-axis
D. (d) fixed radius 1 and variable centres along the Y-axis

Answer

(c)

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`
Here, centre(-c,0) and radius = 1