F为抛物线y²=4x的焦点,A,B,C为抛物线上三点,O为坐标原点若F为△ABC的重心,△OFA,△OFB,△OFC的面积分别为S1,S2,S3,则S1²+S2²+S3²=
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![F为抛物线y²=4x的焦点,A,B,C为抛物线上三点,O为坐标原点若F为△ABC的重心,△OFA,△OFB,△OFC的面积分别为S1,S2,S3,则S1²+S2²+S3²=](/uploads/image/z/5301663-15-3.jpg?t=F%E4%B8%BA%E6%8A%9B%E7%89%A9%E7%BA%BFy%26%23178%3B%EF%BC%9D4x%E7%9A%84%E7%84%A6%E7%82%B9%2CA%2CB%2CC%E4%B8%BA%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8A%E4%B8%89%E7%82%B9%2CO%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%E8%8B%A5F%E4%B8%BA%E2%96%B3ABC%E7%9A%84%E9%87%8D%E5%BF%83%2C%E2%96%B3OFA%2C%E2%96%B3OFB%2C%E2%96%B3OFC%E7%9A%84%E9%9D%A2%E7%A7%AF%E5%88%86%E5%88%AB%E4%B8%BAS1%2CS2%2CS3%2C%E5%88%99S1%26%23178%3B%2BS2%26%23178%3B%2BS3%26%23178%3B%3D)
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F为抛物线y²=4x的焦点,A,B,C为抛物线上三点,O为坐标原点若F为△ABC的重心,△OFA,△OFB,△OFC的面积分别为S1,S2,S3,则S1²+S2²+S3²=
F为抛物线y²=4x的焦点,A,B,C为抛物线上三点,O为坐标原点
若F为△ABC的重心,△OFA,△OFB,△OFC的面积分别为S1,S2,S3,则S1²+S2²+S3²=
F为抛物线y²=4x的焦点,A,B,C为抛物线上三点,O为坐标原点若F为△ABC的重心,△OFA,△OFB,△OFC的面积分别为S1,S2,S3,则S1²+S2²+S3²=
可知焦点F坐标为(1,0)
以OF为底,即底为1 所以△OFA,△OFB,△OFC的高分别分别Ya,Yb,Yc
即S1²+S2²+S3²=(Y²a+Y²b+Y²c)/4
因为F为△ABC的重心,根据在平面直角坐标系中,重心的坐标是顶点坐标的算术平均即(Xa+Xb+Xc)/3=1,(Ya+Yb+Yc)/3=0 可知Xa+Xb+Xc=3 因为y²=4x 又有Y²a+Y²b+Y²c=3*4=12
所以S1²+S2²+S3²=12/4=3