以椭圆9x2+4y2=36的长轴端点为短轴端点，且过点（-4，1）的椭圆

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问题填空题

以椭圆9x²+4y²=36的长轴端点为短轴端点，且过点（-4，1）的椭圆标准方程是______．

答案

椭圆9x²+4y²=36化成标准方程，得

∴椭圆9x²+4y²=36长轴的端点坐标为：（0，±3）

因此可设所求的椭圆方程为

∵经过点（-4，1），

∴

=1，解之得a²=18

因此，所求椭圆标准方程是

故答案为：

填空题

用所给单词的适当形式填空。

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