F为y^2=4x焦点,A,B,C为其上三点,FA+FB+FC=0,OFA,OFB,OFC的面积为S1,S2,S3,求(S1)2+(S2)2+(S3)设F为抛物线y^2=4x的焦点,A,B,C为该抛物线上三点,O为坐标原点,若向量FA+向量FB+向量FC=向量0,三角形OFA,OFB,
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![F为y^2=4x焦点,A,B,C为其上三点,FA+FB+FC=0,OFA,OFB,OFC的面积为S1,S2,S3,求(S1)2+(S2)2+(S3)设F为抛物线y^2=4x的焦点,A,B,C为该抛物线上三点,O为坐标原点,若向量FA+向量FB+向量FC=向量0,三角形OFA,OFB,](/uploads/image/z/14508613-37-3.jpg?t=F%E4%B8%BAy%5E2%3D4x%E7%84%A6%E7%82%B9%2CA%2CB%2CC%E4%B8%BA%E5%85%B6%E4%B8%8A%E4%B8%89%E7%82%B9%2CFA%2BFB%2BFC%EF%BC%9D0%2COFA%2COFB%2COFC%E7%9A%84%E9%9D%A2%E7%A7%AF%E4%B8%BAS1%2CS2%2CS3%2C%E6%B1%82%EF%BC%88S1%EF%BC%892%2B%EF%BC%88S2%EF%BC%892%2B%EF%BC%88S3%EF%BC%89%E8%AE%BEF%E4%B8%BA%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D4x%E7%9A%84%E7%84%A6%E7%82%B9%2CA%2CB%2CC%E4%B8%BA%E8%AF%A5%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%2C%E8%8B%A5%E5%90%91%E9%87%8FFA%2B%E5%90%91%E9%87%8FFB%2B%E5%90%91%E9%87%8FFC%EF%BC%9D%E5%90%91%E9%87%8F0%2C%E4%B8%89%E8%A7%92%E5%BD%A2OFA%2COFB%2C)
F为y^2=4x焦点,A,B,C为其上三点,FA+FB+FC=0,OFA,OFB,OFC的面积为S1,S2,S3,求(S1)2+(S2)2+(S3)设F为抛物线y^2=4x的焦点,A,B,C为该抛物线上三点,O为坐标原点,若向量FA+向量FB+向量FC=向量0,三角形OFA,OFB,
F为y^2=4x焦点,A,B,C为其上三点,FA+FB+FC=0,OFA,OFB,OFC的面积为S1,S2,S3,求(S1)2+(S2)2+(S3)
设F为抛物线y^2=4x的焦点,A,B,C为该抛物线上三点,O为坐标原点,若向量FA+向量FB+向量FC=向量0,三角形OFA,OFB,OFC的面积分别为S1,S2,S3,则(S1)^2+(S2)^2+(S3)^2D的值是(____)?
A,9 B,6 C,4 D,3
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F为y^2=4x焦点,A,B,C为其上三点,FA+FB+FC=0,OFA,OFB,OFC的面积为S1,S2,S3,求(S1)2+(S2)2+(S3)设F为抛物线y^2=4x的焦点,A,B,C为该抛物线上三点,O为坐标原点,若向量FA+向量FB+向量FC=向量0,三角形OFA,OFB,
依题设设A,B,C三点的坐标分别为A(y1^2/4,y1),B(y2^2/4,y2),C(y3^2/4,y3),因为抛物线的焦点为F(1,0),所以 向量FA+向量FB+向量FC
=((y1^2/4)-1,y1)+((y2^2/4)-1,y2)+((y3^2/4)-1,y3)
=([(y1^2+y2^2+y3^2)/4]-3,y1+y2+y3)
=(0,0)
所以[(y1^2+y2^2+y3^2)/4]-3=0,解得y1^2+y2^2+y3^2=12
因为三个三角形同底OF=1,所以(S1)^2+(S2)^2+(S3)^2
=(1/4)*(y1^2+y2^2+y3^2)
=12/4=3
故选D.