若抛物线y²=x上一点P到准线的距离等于它到顶点的距离，则点P的坐标为（   ）

A：$\left(\frac{1}{4},\pm \frac{\sqrt{2}}{4}\right)$

B：$\left(\frac{1}{8},\pm \frac{\sqrt{2}}{4}\right)$

C：$\left(\frac{1}{4},\frac{\sqrt{2}}{4}\right)$

D：$\left(\frac{1}{8},\frac{\sqrt{2}}{4}\right)$