Releted Question 1
Consider a circle with its centre lying on the focus of the parabola $${y^2} = 2px$$ such that it touches the directrix of the parabola. Then a point of intersection of the circle and parabola is-
A.
$$\left( {\frac{p}{2},\,p} \right){\text{ or }}\left( {\frac{p}{2},\, - p} \right)$$
B.
$$\left( {\frac{p}{2},\, - \frac{p}{2}} \right)$$
C.
$$\left( { - \frac{p}{2},\,p} \right)$$
D.
$$\left( { - \frac{p}{2},\, - \frac{p}{2}} \right)$$