Question

与椭圆x2/4+y2/3=1,具有相同的离心率且过点（2,负的根号3）的椭圆的标准方程：

Answer 1

a'�0�5=4,b'�0�5=3
c'�0�5=1
e'=c'/a'=1/2

则所求椭圆e=1/2=c/a
a=2c
b�0�5=a�0�5-c�0�5=3c�0�5
所以是x�0�5/4c�0�5+y�0�5/3c�0�5=1或y�0�5/4c�0�5+x�0�5/3c�0�5=1
把点代入
x�0�5/4c�0�5+y�0�5/3c�0�5=1
4/4c�0�5+3/3c�0�5=1
c�0�5=2

y�0�5/4c�0�5+x�0�5/3c�0�5=1
3/4c�0�5+4/3c�0�5=1
c�0�5=25/12

所以
x�0�5/8+y�0�5/6=1和3y�0�5/25+4x�0�5/25=1