Ratio of Squares of Integers of Opposite Signs

From $(a + 3)^2 / b^2 = 9 \implies a + 3 = \pm 3b$. From $(a - 1)^2 / (b - 1)^2 = 4 \implies a - 1 = \pm 2(b - 1)$. Since $a, b$ are integers of opposite signs, test $a + 3 = -3b \implies a = -3b - 3$. Substitute into $a - 1 = 2(b - 1) \implies -3b - 4 = 2b - 2 \implies 5b = -2$ (not integer). Test $a - 1 = -2(b - 1) = -2b + 2 \implies -3b - 4 = -2b + 2 \implies b = -6 \implies a = 15$. Opposite signs check: $a = 15, b = -6$ are opposite signs. $(a+3)^2 : b^2 = 18^2 : (-6)^2 = 324 : 36 = 9 : 1$. $(a-1)^2 : (b-1)^2 = 14^2 : (-7)^2 = 196 : 49 = 4 : 1$. $a^2 : b^2 = 15^2 : (-6)^2 = 225 : 36 = 25 : 4$.