The solution of `dy/dx = (x^2+y^2+1)/(2xy)` satisfying `y(1)=0` is given by

Options

A. hyperbola
B. circle
C. ellipse
D. parabola

Answer

d

Explanation

`(dy)/(dx) = (x^(2)+y^(2)+1)/(2xy)`
` rArr 2xydy = (x^(2) +1) dx +y^(2)dx`
` rArr (xd(y^(2))-y^(2)dx)/(x^(2)) = ((x^(2)+1)/(x^(2)))dx`
` rArr int d ( y^(2) //x) = int (1+1/(x^(2)))dx rArr (y^(2))/x = x - 1/x +C`
` rArr y^(2) = (x^(2) - 1+Cx)`
Given, x=1 , y = 0
` :. 0 = 1 - 1 +C rArr C = 0 `
` rArr y^(2) = x^(2) -1 rArr x^(2) - y^(2) =1`
which is the equation of a hyperbola .