Question

1．根据下列条件,求双曲线的标准方程：1．根据下列条件,求双曲线的标准方程：

Answer 1

c=6

c^2=a^2+b^2=36

(-5,2)代入方程：x^2/a^2-y^2/b^2=1

25/a^2-4/b^2=1

25/a^2-4/(36-a^2)=1

25(36-a^2)-4a^2=a^2(36-a^2)

900-29a^2=36a^2-a^4

a^4-65a^2+900=0

(a^2-45)(a^2-20)=0

a^2=45,or,a^2=20

b^2=-9(舍）,or,b^2=16

方程是：x^2/20-y^2/16=1