JEE Advance - Mathematics (1995 - No. 17)
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
$$\left( {{p \over 2},p} \right)$$ or $$\left( {{p \over 2},- p} \right)$$
$$\left( { {p \over 2}, {p \over 2}} \right)$$
$$\left( -{{p \over 2},p} \right)$$
$$\left( { - {p \over 2}, - {p \over 2}} \right)$$