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Topic: sum and difference locus is same parabola?
Replies: 3   Last Post: Jan 28, 2011 6:54 AM

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narasimham

Posts: 2,537
Registered: 12/6/04
sum and difference locus is same parabola?
Posted: Dec 18, 2010 12:18 PM
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Point P(0,a) is on y-axis, point M (x,0) is on x-axis, P is in x-y
plane.

If the sum of distances PM and PF equals s, locus of P is

y + sqrt( (y-a)^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






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