The curve satisfying the eqn

dy / dx = (y² - 2xy - x²) / (y² + 2xy - x²) passes through (-1, 1) is a

(a) staight line (b) circle (c) ellipse (d) none of these

Dear Sanchit Gupta

dy / dx = (y² - 2xy - x²) / (y² + 2xy - x²)

Let y=vx

dy/dx =v+xdv/dx

so v+x dy/dx =(v² - 2v -1) / (v² + 2v - 1)

x dv/dx =(v² - 2v -1) / (v² + 2v - 1)     -v

x dv/dx = -(v3 +v2 +v +1)/(v² + 2v - 1)

(v² + 2v - 1)/(v3 +v2 +v +1)  dv =-dx/x

Now variable are seperated you can solve the differential equation