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85问答库 > 长轴长是短轴长的3倍，且经过点P（3,0）求适合条件的椭圆标准方程

长轴长是短轴长的3倍，且经过点P（3,0）求适合条件的椭圆标准方程

2025-03-25 12:01:15

推荐回答（2个）

回答1：

分情况讨论
⑴当焦点在x轴时候，则b=3，此时a=9
∴椭圆为x²/81+b²/9=1
⑵当焦点在y轴时，a=3，此时b=1
椭圆方程为y²/9+x²=1

回答2：

设短轴为a,则长轴为3a经过点P（3,0）,可得：
3^2/9a^2+0^2/a^2=1
解得：a^2=1
所以有：x^2/9+y^2=1
或：
3^2/a^2+0^2/9a^2=1
解得：a^2=9
所以有：x^2/9+y^2/81=1

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