经过点A(-2/3,5/2)与B(√3.√5,)的椭圆标准方程请写明化简过程

Question

经过点A(-2/3,5/2)与B(√3.√5,)的椭圆标准方程
请写明化简过程

Answer 1

x^2/a^2+y^2/b^2=1
代入
(4/9)/a^2+(25/4)/b^2=1
1/a^2+(225/16)/b^2=9/4 (1)
3/a^2+5/b^2=1 (2)
(1)*3-(2)
(675/16)/b^2-5/b^2=23/4
(595/16)/b^2=23/4
1/b^2=92/595
1/a^2=9/4-(225/16)/b^2=9/119
x^2/(119/9)+y^2/(595/92)=1