设抛物线的焦点为,过点的直线与抛物线相交于两点,与抛物线的准

设抛物线的焦点为,过点的直线与抛物线相交于两点,与抛物线的准线相交于点,则的面积之__________

答案

【解析】

由题意可得抛物线的焦点的坐标为,准线方程为

如图,设,过A,B分别向抛物线的准线作垂线,垂足分别为E,N,则

,解得

代入抛物线,解得

直线AB经过点与点

故直线AB的方程为,代入抛物线方程解得

中,

。答案:

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