1. The hyperbola

Here's another question that I'm stuck with (again). Can someone help me please?

Q: P is any point on the hyperbola with equation (x^2)/a^2-(y^2)/b^2=1, S is the focus(ae,0) and S' is the focus(-ae,0). Show that

SP-S'P(with the modulus sign) =2a

I'm not really sure where to start, since my usual route of attack, differentiation, has done me no good with this question as it's not related to tangents and normals.

Help would be greatly appreciated.

2. Originally Posted by free_to_fly
Here's another question that I'm stuck with (again). Can someone help me please?

Q: P is any point on the hyperbola with equation (x^2)/a^2-(y^2)/b^2=1, S is the focus(ae,0) and S' is the focus(-ae,0). Show that

SP-S'P(with the modulus sign) =2a

I'm not really sure where to start, since my usual route of attack, differentiation, has done me no good with this question as it's not related to tangents and normals.

Help would be greatly appreciated.
questions: what is "e"? and how do you define SP and S'P?

i suppose |SP - S'P| means the distance between the two points SP and S'P, so it would be something like (using the distance formula) $|SP - S'P| = \sqrt{[ae - (-ae)]^2 + (0 - 0)^2} = 2ae$ or something like that. don't know what all your variables mean, but it should be something along those lines

3. e is the eccentricity of the hyperbola, and I tried the find the lengths SP and S'P using Pythagoras, but the result I got was 4ax[(b^2)/(a^2)]^1/2, I can't see how that's anything like the answer though, so maybe I've used the wrong coordinates for P. I used {x, b[(x^2)/a^2]^1/2}, which came from rearranging the original equation. I must have gone wrong though, oh and I substituted out e using b^2=a^2(e^2-1)