Question

根据下列条件,求出椭圆的标准方程.

Answer 1

c² = 9 - 4 = 5

a² = b² + 5

新椭圆:x²/(b² + 5) + y²/b² = 1

代入M的坐标:9/(b² + 5) + 4/b² = 1

b⁴ - 8b² - 20 = (b² - 10)(b² + 2) = 0

b² = 10 (舍去b² = -2 < 0)

a² = 15

新椭圆的标准方程:x²/15 + y²/10 = 1