The solution of `dy/dx = (x^2+y^2+1)/(2xy)` satisfying `y(1)=0` is given byA. hyperbolaB. circleC. ellipseD. parabola

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

1.	The solution of `dy/dx = (x^2+y^2+1)/(2xy)` satisfying `y(1)=0` is given byA. hyperbolaB. circleC. ellipseD. parabola
Answer» Correct Answer - d `(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 .

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The solution of `dy/dx = (x^2+y^2+1)/(2xy)` satisfying `y(1)=0` is given byA. hyperbolaB. circleC. ellipseD. parabola

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