渐近线y=-1/3x 则
(1)焦点在x轴上,则设x²/a²-y²/(3a)²=1 ∵过(3,2)∴9/a²-4/9a²=1 得a²=77/9
∴双曲线x²/(77/9)-y²/77=1
(2)焦点在y轴上,则设y²/a²-x²/(3a)²=1 ∵过(3,2)∴4/a²-9/9a²=1 得a²=3
∴双曲线y²/3-y²/27=1
渐近线y=-1/3x 则
(1)焦点在x轴上,则设x²/a²-y²/(3a)²=1 ∵过(3,2)∴9/a²-4/9a²=1 得a²=77/9
∴双曲线x²/(77/9)-y²/77=1
(2)焦点在y轴上,则设y²/a²-x²/(3a)²=1 ∵过(3,2)∴4/a²-9/9a²=1 得a²=3
∴双曲线y²/3-y²/27=1