Consider a circle with center lying on the focus of the parabola $ y^2=2px$ Such that it touches the directix of the parabola. Then a point of intersection of the circle and the parabola is

Question

$\begin{array}{1 1} \bigg( \frac{p}{2},P\bigg) \\ \bigg( \frac{p}{2},-p\bigg) \\ \bigg( \frac{p}{2},p\bigg) \\ \bigg( \frac{-p}{2},-p\bigg) \end{array} $