Let f = f(x, y) be a quadratic form with real coefficients in two integer variables x, y. Let V(f) be the set of values taken by f(x, y) at points (x, y) ≠ (0,0). Impose the same conditions on a second form f′. Trivially, f equivalent to f′ implies V(f) = V(f′). It will be shown that the converse implication holds in general for definite forms; the obvious exception f = x2 + xy + y2, f′ = x2 + 3y2 will be shown to be essentially the only one.