A(a^2/2p,a), B(b^2/2p,b), 焦点F(p/2,0) 焦点F是△AOB的重心: p/2 =(a^2/2p +b^2/2p +0)/3, a^2+b^2 =3p^2 ...(1) 0 =(a+b+0)/3, a+b =0 ...(2) 直线AB斜率 =(a-b)/(a^2/2p -b^2/2p) =2p/(a+b) =无穷大 ==> 直线AB垂直X轴 (1) ==> a^2 =b^2 =3p^2/2 直线AB方程：x =a^2/2p, 即：x =3p/4
解：0为原点.|OA|=|OB| ===> A、B关于抛物线对称轴（x轴）对称 设参数坐标A(2pt²,2pt),B(2pt²,-2pt),焦点F(p/2,0) ===> 直线AB的方程: x=2pt² k(OA)=(2pt)/(2pt²)=1/t k(BF)=(-2pt-0)/(2pt²-p/2)=(4t)/(4t²-1) F△AOB是垂心 ===> OA⊥BF ===> k(OA)k(BF)=-1=4/(4t²-1) ===> 4t²-1=4 ===> t²=5/4 ===> 直线AB的方程: x=(5/2)p
答：设A(2pm^2,2pm),则B(2pm^2,-2pm) 直线AB的方程x=2pm^2 焦点F(p/2,0) 直线OA斜率是2pm/2pm^2=1/m 直线BF...详情>>
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