抛物线顶点在原点，焦点在x轴上，且过点（8，8），焦点为F
（1）求抛物线的焦点坐标和标准方程；
（2）P是抛物线上一动点，M是PF的中点，求M的轨迹方程．
（1）抛物线顶点在原点，焦点在x轴上，且过点（8，8），
设抛物线解析式为y2=2px，把（8，8）代入，得，64=2×8p，∴p=4
∴抛物线标准方程为：y2=8x，焦点坐标为F（2，0）
（2）设M（x，y），P（x0，y0），
由
⇒x= x0+2 2 y= y0 2 x0=2x-2 y0=2y
又∵
=8x0，y 20
∴（2y）2=8（2x-2）
∴y2=4（x-1）
∴M的轨迹方程为y2=4x-4．
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