拋物線(xiàn) y²=2px 的焦點(diǎn)為F(p/2,0),設(shè)過(guò)焦點(diǎn)F的直線(xiàn)為 y=kx-kp/2 (k≠0)把直線(xiàn)方程代入拋物線(xiàn)方程,得(kx-kp/2)²=2pxk²x²-(kp+2p)x+k²p²/4=0這個(gè)關(guān)于x的一元二次方程的兩個(gè)根 x1,x2是直...我感覺(jué)k1*k2=y1y2/x1x2=-p^2/(1/4p^2）=-4這里有誤 k²x²-(k²p+2p)x+k²p²/4=0這個(gè)關(guān)于x的一元二次方程的兩個(gè)根 x1,x2是直線(xiàn)與拋物線(xiàn)的兩個(gè)交點(diǎn)A,B 的橫坐標(biāo)∴x1+x2=(k²p+2p)/k²x1x2=p²/4y1y2=(kx1-kp/2)(kx2-kp/2)=k²x1x2-k²p/2(x1+x2)+k²p²/4 =k²p²/4-k²p/2（k²p+2p)/k²+k²p²/4 =k²p²/2-k²p²/2-p²=p²(k²-k²-2)/2=-p²∵OA 的斜率是k1=y1/x1 OB 的斜率是k2=y2/x2∴k1k2=(y1y2)/(x1x2)=(-p²)/(p²/4) =-4sorry