Aditya Gupta
Last Activity: 6 Years ago
consider a parabola y^2=4ax; a>0, with focus (a,0) and tangent to the vertex being x=0
now, let a focal chord intersect the parabola at (at^2, 2at) and (ap^2, 2ap)
as this chord passes thru focus, we have
[2ap-2at]/[ap^2-at^2]=2ap/[ap^2-a]
or pt= –1
or p^2t^2=1
now, the lengths from the tangent at vertex are:
at^2, a, ap^2
we see that a/at^2=ap^2/a
so, the lengths are in GP
