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...