
sum and difference locus is same parabola?
Posted:
Dec 18, 2010 12:18 PM


Point P(0,a) is on yaxis, point M (x,0) is on xaxis, P is in xy plane.
If the sum of distances PM and PF equals s, locus of P is
y + sqrt( (ya)^2 +x^2 ), or,
2 y = s  (x^2 +a^2 2 a y)/s.
If the difference of distances PM and PF equals s,
then also locus of P, due to squaring of the square root, again is:
2 y = s  (x^2 +a^2 2 a y)/s.
How can both loci be the same ?
Regards
Narasimham

