椭圆面积能这么求吗椭圆x²/a²+y²/b²=1圆x²/a²+y²/a²=1所以S椭圆=S圆*b/a=πab
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![椭圆面积能这么求吗椭圆x²/a²+y²/b²=1圆x²/a²+y²/a²=1所以S椭圆=S圆*b/a=πab](/uploads/image/z/13514665-49-5.jpg?t=%E6%A4%AD%E5%9C%86%E9%9D%A2%E7%A7%AF%E8%83%BD%E8%BF%99%E4%B9%88%E6%B1%82%E5%90%97%E6%A4%AD%E5%9C%86x%26%23178%3B%2Fa%26%23178%3B%2By%26%23178%3B%2Fb%26%23178%3B%3D1%E5%9C%86x%26%23178%3B%2Fa%26%23178%3B%2By%26%23178%3B%2Fa%26%23178%3B%3D1%E6%89%80%E4%BB%A5S%E6%A4%AD%E5%9C%86%3DS%E5%9C%86%2Ab%2Fa%3D%CF%80ab)
椭圆面积能这么求吗椭圆x²/a²+y²/b²=1圆x²/a²+y²/a²=1所以S椭圆=S圆*b/a=πab
椭圆面积能这么求吗
椭圆x²/a²+y²/b²=1
圆x²/a²+y²/a²=1
所以S椭圆=S圆*b/a=πab
椭圆面积能这么求吗椭圆x²/a²+y²/b²=1圆x²/a²+y²/a²=1所以S椭圆=S圆*b/a=πab
可以啊,这个是椭圆的面积公式.
考虑1/4椭圆(在第一象限),设面积是S1
x²/a²+y²/b²=1
y=(b/a)√(a²-x²)
∴ S1=∫[0,a] (b/a)√(a²-x²)dx
=(b/a) ∫[0,a] √(a²-x²)dx
利用定积分的几何意义,∫[0,a] √(a²-x²)dx=πa²/4
∴ S1=πab/4
∴ 椭圆面积S=πab