Consider the set of all points P(x,y) that are equidistant from the point F(2,0) and the line x=−2.
(i) Show that the vertex of the curve lies at the origin.
(ii) Find the Cartesian equation of the curve.
(iii) State the coordinates of its focus, the equation of its directrix, and the length of its latus rectum.
(iv) Sketch the curve on the Cartesian plane, clearly marking the focus, directrix and vertex.