Question

求焦点为F1(0,-6),F2（0,6）,且过点M（2,5）的双曲线的标准方程.

Answer 1

焦点为F1(0,-6),F2（0,6）,

c=6,焦点在y轴

y^2/b^2-x^2/a^2=1

a^2+b^2=c^2

b^2=36-a^2

把M代入

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

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

a^4-7a^2-144=0

(a^2-16)(a^2+9)=0

a^2>0

a^2=16

b^2=20

所以y^2/20-x^2/16=1