Intersection of a line and a parabola

Intersection of Ellipse with Parabola

Parabola- common tangent OF two curves || Point OF intersection OF tangents OF a parabola || Equation OF normal OF a parabola

Intersection of Parabola with Parabola

LetS={(x,y)|x^(2)+2xy+y^(2)-3x-3y+2=0}, thenS vdots(A) consists of two coincident lines.(B) consists of two parallel lines which are not coincident.(C) consists of two intersecting lines.(D) is a parabola.

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 a point of intersection of the circle & the parabola is: