concepts

Check this out>>>

http://chestofbooks.com/architecture/American-House-Carpenter/The-Parabola-Part-2.html

im not getting ur site can u give d direct soution

assume the two pts to be t1 and t2....(parametrically) and the pt at which their normals meet to be t
now we have ,
2/(t+t1) =-t1-----1) (slope of the t1,t line)
and also 2/(t+t2)=-t2----2)
let the midpt be (h,k)
we have h=(a(t1²+t2²)/2)-----6)
and k=(a(t1+t2))-------5)
from 1 and 2, we have
-2/t1 =t+t1------3)
and
-2/t2=t+t2------4)
now subtracting 4) from 3) we have
2(1/t2 - 1/t1) =t1-t2
or 2/t1t2 =1
t1t2=1
now from 5 and 6 we know that t1t2= [{k/a}²-2(h/a)]/2
so we have the reqd locus is that,
4a²=k²-2ah...
this cud have been done much easily if one knew the property of t1t2=2 from before...