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结论把圆x~2+y~2=a~2按b/a压缩成椭圆(x~2)/(a~2) +(y~2)/(b~2)=1,则可得椭圆的面积S=πab.如何理解?直观的解释是:椭圆的长短轴之比a/b,椭圆按cosθ=b/a,投影到水平面α上得半径为a的圆如图.∴S_(椭圆)=b/aS_圆=b/aπa~2=πab.
Conclusion Compressing the circle x ~ 2 + y ~ 2 = a ~ 2 into an ellipse (x ~ 2) / (a ~ 2) + (y ~ 2) / (b ~ 2) = 1 according to b / The oval area S = πab. How to understand? Intuitive explanation is: the length of the ellipse axis ratio a / b, ellipse by cosθ = b / a, projected onto the horizontal surface α radius of a circle shown in Figure. Ellipse) = b / aS_ circle = b / aπa ~ 2 = πab.