已知在平面直角坐标系xOy中,抛物线y^2=2px(P>0)的焦点是F,过抛物线的准线与x轴交点的直线与抛物线交于A,B两点,1)求OA向量*OB向量的值.2)求证角AFB被过F且垂直于x轴的直线l平分.
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![已知在平面直角坐标系xOy中,抛物线y^2=2px(P>0)的焦点是F,过抛物线的准线与x轴交点的直线与抛物线交于A,B两点,1)求OA向量*OB向量的值.2)求证角AFB被过F且垂直于x轴的直线l平分.](/uploads/image/z/12573825-33-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%A8%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BBxOy%E4%B8%AD%2C%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D2px%28P%3E0%29%E7%9A%84%E7%84%A6%E7%82%B9%E6%98%AFF%2C%E8%BF%87%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E5%87%86%E7%BA%BF%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E7%82%B9%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C1%EF%BC%89%E6%B1%82OA%E5%90%91%E9%87%8F%2AOB%E5%90%91%E9%87%8F%E7%9A%84%E5%80%BC.2%EF%BC%89%E6%B1%82%E8%AF%81%E8%A7%92AFB%E8%A2%AB%E8%BF%87F%E4%B8%94%E5%9E%82%E7%9B%B4%E4%BA%8Ex%E8%BD%B4%E7%9A%84%E7%9B%B4%E7%BA%BFl%E5%B9%B3%E5%88%86.)
已知在平面直角坐标系xOy中,抛物线y^2=2px(P>0)的焦点是F,过抛物线的准线与x轴交点的直线与抛物线交于A,B两点,1)求OA向量*OB向量的值.2)求证角AFB被过F且垂直于x轴的直线l平分.
已知在平面直角坐标系xOy中,抛物线y^2=2px(P>0)的焦点是F,过抛物线的准线与x轴交点的直线与抛物线交于A,B两点,
1)求OA向量*OB向量的值.
2)求证角AFB被过F且垂直于x轴的直线l平分.
已知在平面直角坐标系xOy中,抛物线y^2=2px(P>0)的焦点是F,过抛物线的准线与x轴交点的直线与抛物线交于A,B两点,1)求OA向量*OB向量的值.2)求证角AFB被过F且垂直于x轴的直线l平分.
1)设直线x=y/k-p/2,A(x1,y1),B(x2,y2)
代入抛物线方程得
y^2-2py/k+p^2=0
∴y1*y2=p^2
∴OA向量*OB向量=x1*x2+y1*y2=(y1)^2*(y2)^2/(4p^2)+y1*y2=(5p^2)/4
2)设l与AB交与C
∴C(p/2,kp)
然后证明AC/BC=AF/BF即可推出l平分角AFB