A parabola has its focus at the point (3,0) and its directrix is the line x=−3.
(i) Using the definition of a parabola, derive its Cartesian equation in standard form.
(ii) From the equation obtained, write the coordinates of the vertex and the equation of the axis.
(iii) Find the coordinates of the end-points of the latus rectum and hence its length.
(iv) Verify that the length obtained in part (iii) equals 4a, where a is the parameter appearing in your equation from part (i).