Prove that the equation of a curve whose slope at `(x,y)` is `-(x+y)/x` and which passes through the point `(2,1)` is `x^2+2xy=8`

Find the equation of the curve whose slope at any point (x,y) is (-y) and which through the point (2,1)

Find the equation of the curve whose slope is (y-1)/(x^(2)+x) and which passes through the point (1,0).

Find the equation of the curve whose gradient at (x,y) is y/(2x) and which passes through the point (a,2a) .

Find the equation of the curve whose gradient at (x,y) is y/(2x) and which passes through the point (a,2a) .

Let y=y(x) be the equation of a curve whose slope at (x,y) is -((x+y))/(x) and which passes through the point (2,1) .Then value of y(1) is

The equation of the curve whose slope is given by (dy)/(dx)=(2y)/x ; x >0,\ y >0 and which passes through the point (1,1) is