Question

等腰直角三角形AOB内接于抛物线y²=2px(p＞0)，O为抛物线的顶点，OA⊥OB，则△AOB的面积是

A.8p²                                                              B.4p²

C.2p²                                                              D.p²

Answer 1

解析:∵抛物线的对称轴为x轴，内接△AOB为等腰直角三角形，∴由抛物线的对称性知，直线AB与抛物线的对称轴垂直，从而直线OA与x轴的夹角为45°.

由方程组得或

∴A、B两点的坐标分别为(2p,2p)和(2p,－2p).

∴|AB|=4p.∴S_△AOB=×4p×2p=4p².

答案:B