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.

解析:

(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.