课本中推导椭圆标准方程的计算量大而繁,若能抓住椭圆定义中|MF_1|+|MF_2|=2a(a＞0),构造等差数列,则可巧妙而简捷地推导椭圆的标准方程。由椭圆的定义,按教材中的方法建立直角坐标系,得方程：(?) ∴ (?)成等差数列,设公差为d,则有①~2-②~2,得 4cx=4ad, 即 d=(c/a)x ③ The computational complexity of deducing elliptic standard equations in textbooks is large and complex. If we can seize the | MF_1 | + | MF_2 | = 2a (a> 0) in the ellipse definition and construct the arithmetic progression, we can ingeniously and concisely deduce the standard of ellipse equation. The definition of the ellipse, according to the method of teaching materials to establish rectangular coordinate system, the equation: (?) ∴ (?) Into arithmetic sequence, set the tolerance of d, then ① ~ 2-② ~ 2, 4cx = 4ad, That is, d = (c / a) x ③