conics question (1 Viewer)

[doiyoubi]

P lies on the hyperbola x²/9 - y²/72 = 1 with foci S and S'
(a) If PS=2 find PS'
(b) If PS=8 find PS'

I've tried and tried but I don't think this is even possible

 

[Trev]

Well, remember the identity PS-PS'=2a? It's simple from there.

 

[Riviet]

You can prove that result using the definition of a hyperbola.

 

[doiyoubi]

The answer for part (i) is 8 yet using that theorem I get -4 using the hyperbola theorem of PS-PS'=2a

 

[cyl123]

remember its | PS - PS' | =2a
So you have 2 cases, one getting 8 and other getting -4
As PS' is a distance so it is positive so therefore the answer is 8