Question

For an ellipse, where k is the sum of distance from any P(x,y) to its focal points, for what values of k will the locus be an ellipse, a line segment(what is the equation of the line), or the nullset?

Answer 1

What about for hyperbolas, k=difference of distance between P and F F'. What values of k will the locus be a hyperbola,pair of rays(equation of each ray), null set?
Can you have negative distance?

Answer 2

Try asking this in MIT 8.01 or MIT Physics.

Answer 3

I don't understand, the sum of the distances to the foci is equal to 2a
ie Pf1 + Pf2 = 2a
That's a definition for an ellipse.

Answer 4

ok how about
for what values of k, sum of distance between focal points and points(x,y), will the locus of the point be an ellipse, a line segment, or null set.
e.g. let distance between foci=2c
ellipse:k>2c line segment:k=2c y=0 F'(x)<=x<=F(x), x=0 F'(y)<=y<=F(x)
nullset:k<2c
is that right

Answer 5

asdsadasd

Answer 6

did i accidentally close my question..

Answer 7

It's Ok, I was on the phone, just reading it now...

Answer 8

"for what values of k, sum of distance between focal points and points(x,y), will the locus of the point be an ellipse, a line segment, or null set."

The sum you are talking about is equal to 2a

Answer 9

okso.. a^2=b^2+c^2 for ellipse so a>c.. yeah?

Answer 10

and 2c>2a .: k<2c for hyperbola

Answer 11

Usually it is written c^2 = a^2-b^2 but I prefer to think directly of the eccentricity e
ie focus plusminus ae and e = sqrt(1-b^2/a^2)

Answer 12

or 1+b^2/a^2 for hyperbola

Answer 13

so.. for hyperbolas for what values of k will it exist as ahyperbola pair of ray or null set

Answer 14

Define k

Answer 15

PF'-PF=k

Answer 16

P(x,y) F'(focal points)

Answer 17

I should have never posted on this thread. I keep getting notifications. :(

Answer 18

sorry :x

Answer 19

Are we talking about ellipse or hyperbola?

http://en.wikipedia.org/wiki/Hyperbola#Difference_of_distances_to_foci
http://en.wikipedia.org/wiki/Ellipse#Elements_of_an_ellipse

Answer 20

hyperbola

Answer 21

how about.. for what values of k is the locus of P(x,y) PF'-PF=k a hyperbola, pair of rays, null set.

Answer 22

I think what you should do is post your question as a new question (this will stop the notifications and bring other people to the question)