f(x,y)g(x,y)h(x,y)=nx2+(2nm)xy+my2+4x+2y+1=0=nx2+(n+m)xy+my2+4x+2y+1=0=nx2+(n−m)xy+my2+4x+2y+1=0
Let the graphs f,g,h be a parabola, a hyperbola, and an ellipse, respectively.
If n and m are positive integers satisfying the constraints above, compute 2n+m.