Hi Peeps,

I was wondering if you guys could provide me with a really hard question concerning parametric equations and the loci. Preferably something that involves a parabola and is similar to the format of this question:

"Find the equation of the locus of the midpoint M of all chords PQ where P(2ap, ap^2) and Q(2aq, aq^2) lie on the parabola x^2=4ay, and PQ passes through (0, 2a)."

I'm personally looking for something very challenging and that calls upon the use of other coordinate geometry properties, e.g. midpoints, perpendicular lines, etc...

Many thanks,

ekfteo