有两道题目跪求高手解答，急需！！！考虑到数学符号难打，麻烦写在自己纸上，然后拍照到发1043599765邮箱

觉得这样挺清楚，否则再问行余

1.
(1) 椭圆的焦点在x轴上，设椭圆方程x²/a² + y²/b² = 1, a >b (i)
焦距2c = 2, c = 1, c² = a² - b², a² = b² + 1
代入(1): x²/(b² + 1) + y²/b² = 1 (ii)
将A(-1, 3/2)代型春入(2)并整理得: 4b⁴ - 9b² - 9 =0
(4b² + 3)(b² - 3) = 0
b² = -3/4 (舍去)
b² = 3, a² = 4
椭圆方程: x²/4 + y²/3 = 1

(2)
a = 2, b = √3
顶点: (-2, 0), (2, 0), (0, -√3), (0, √3)
长轴= 2a = 4
短轴 = 2b = 2√3
离心率 = c/a = 1/2

2.
(1) 焦点在y轴档租滚上，设方程为: y²/a² - x²/b² = 1
F1(0, -4), F2(0, 4), c = 4
c² = a² + b² = 16, b² = 16 - a²
y²/a² - x²/(16 - b²) = 1
代入P(2√2, -6)并整理得: a⁴ - 60a² + 576 =0
(a² - 48)(a² - 12) = 0
a² = 48, b² = 16 - 48 < 0, 舍去
a² = 12, b² = 16 - 12 = 4
双曲线方程: y²/12 - x²/4 = 1

(2)焦点在y轴上，对称轴为坐标轴时的标准方程为: y²/a² - x²/b² = 1
代入两点的坐标:
32/a² - 9/b² = 1 (i)
25/a² - 81/(16b²) = 1 (ii)
(ii) - 16*(i): a² = 16
b² = 9
双曲线方程: y²/16 - x²/9 = 1

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