Question

已知椭圆的中心在原点,焦点在坐标轴上,分别根据下列条件求椭圆的标准方程.
(1)长轴、短轴长之比为2∶1,一条准线为x+4=0;
(2)离心率为,一条准线为y=3.

Answer 1

1、椭圆方程为=1.
2、椭圆方程为=1.

(1)由题意得=2,即a="2b.                                             " ①
∵x=-=-4,即a²="4c,                                                        " ②
又a²=b²+c²,                                                                   ③
解①②③得
∴椭圆方程为=1.
(2)由题意得e==,                                                        ⑤
y=="3.                                                                    " ⑥
由⑤⑥得
∴b²=a²-c²=.
∴椭圆方程为=1.