Name of XY + aX + bY = c

[sql_lall]

Ok, i have an equation:

XY + aX + bY = c

where a,b,c are given integral constants.
What type of equation is this?

Is it linear (cos the highest power of each variable is one), quadratic (cos the highest COMBINED power is 2) or something else?

[twanvl]

I'd say it's neither. You can rewrite it like:
XY + aX + bY = c
(X+b)Y + aX - c = 0
Y = (c-aX)/(X+b)

That is not a polynomial. Just call it an 'equation'

[TheManWhoCan]

It's a "bivariate" polynomial. It's degrees w.r.t. X and Y are both 1, and they add to give the overall order as 2.

[bugzpodder]

i believe this is a translated rectangular hyperbola which means its a conic section. it is definately a second degree, and if the solutions are integers (i assume thats where you are going with integer coefficients) then we call it diophantine equation