Equation of given parabola is y2=2px having focus F(‌
p
2
,0) and equation of directrix is x+‌
p
2
=0, so equation of circle having centre (‌
p
2
,0) and radius r=p, because the circle touches the directrix of the given parabola, is (x−p∕2)2+y2=p2...(i) Now, on solving the equation of the given parabola and circle (i), we get
(x2−px+‌
p2
4
)+2px=p2⇒(x2+px+‌
p2
4
)=p2 ⇒‌‌(x+‌
p
2
)2=p2⇒x+‌
p
2
=±p
⇒‌‌x=‌
p
2
 [∵xp>0] and y=±p Point of intersections of circle and parabola are (‌