*pokes title*
The question is:
P is any point on the hyperbola with the equation
. S is the focus
and S' is the focus
, where e is the eccentricity. Show that
Mr F says: This is wrong. It should be 2ae. You can see this for yourself by taking P(a, 0) and P'(-a, 0) ...... It's ....
My working:
I've found the length ofSP and S'P using good old Pythagoras
, so
and similarly
, which gives me
If one of the signs changes in SP or S'P then I'd get the right answer. Can someone please check if I made a mistake with the signs? Thanks.