Question

已知橢圓的中心在原點,焦點在坐標軸上,分別根據下列條件求橢圓的標準方程.
(1)長軸、短軸長之比為2∶1,一條準線為x+4=0;
(2)離心率為,一條準線為y=3.

Answer 1

1、橢圓方程為=1.
2、橢圓方程為=1.

(1)由題意得=2,即a="2b.                                             " ①
∵x=-=-4,即a²="4c,                                                        " ②
又a²=b²+c²,                                                                   ③
解①②③得
∴橢圓方程為=1.
(2)由題意得e==,                                                        ⑤
y=="3.                                                                    " ⑥
由⑤⑥得
∴b²=a²-c²=.
∴橢圓方程為=1.