Question

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

Answer 1

k must be >0

Answer 2

for what

Answer 3

I'm still having a mental block with this:-

If P is on the hyperbola and the F's are the foci then k is 2a (ie constant) by definition

Answer 4

what happens to the hyperbola when 2a=2c

Answer 5

You hace c^2 = a^2-b^2
For c to equal a then b must be 0

Answer 6

so the hyperbola becomes a line segment along x axis.. yeah?

Answer 7

No, it is just not a hyperbola

Answer 8

so do u get my queston now? :x

Answer 9

No, a hyperbola (centred on (0,0) is x^2/a^2-y^2/b^2 = 1 (b cannot be 0)

Answer 10

the locus doesnt have to be a hyperbola?
for what values of k is the locus of P(x,y) PF'-PF=k a hyperbola, pair of rays, null set.

Answer 11

a>b>0 is part of the definition of a hyperbola

Answer 12

In your question, k=2a and is constant

Answer 13

I think you are trying to ask a different question.

Answer 14

but when k=2a=2c, hyperbola does not exist

Answer 15

a=c is not defined for hyperbola

Answer 16

k>c for locus to be hyperbola. what happens when k=c? should be a pair of rays

Answer 17

Why are you making up definitions for hyperbola, there are standard definitions to use.

Answer 18

Any other definition will not be a hyperbola

Answer 19

im not.. it was a question my test which asked that. it deosnt have to be a hyperbola

Answer 20

Well, that's a different question.......

But you are using P(x,y) which is the usual notation for a point on a hyperbola and F, the usual notation for a focus.

Answer 21

ie you are assuming a hyperbgola to start with.

Answer 22

how about.. when k=2c for sum of distances, the locus is a line segment