The equation of curve through point (1,0) which satisfies the differential equation `(1+y^(2))dx- xy ` dy = 0 , is

Options

A. `x^(2)+y^(2)=4`
B. `x^(2)-y^(2)=1`
C. `2x^(2)+y^(2)=2`
D. None of the above

Answer

c

Explanation

Given , `(dx)/(x) = (ydx)/(1+y^(2))`
` rArr log x = 1/2 log (1+y^(2))+log C rArr x = C sqrt(1+y^(2))`
But it passes through (1,0) ,so we get C = 1
` :. " Solution is " x^(2) - y^(2) = 1`