Conics some1 plz help cos im dumb (1 Viewer)

[raymond0318]

with focus at S and S'
If PS=8 find PS'

I got 14, but the answer says 2 or 14

this is Cmabridge last question exercise 3.1
Thanks

 

[Aesytic]

this conic is a hyperbola branching sideways i.e. x^2 is positive
therefore the focus is S(+-ae,0)
i think where you got lost is assuming that S could only be +ae, when it could actually be -ae as well since the question doesn't specify that S is +ae and S' is -ae [i.e. it could be that S is -ae and S' is +ae instead]
as a result, you end up with 2 possible solutions for PS' if PS=8, one where S(+ae,0) S'(-ae,0) or one where S(-ae,0) S'(+ae,0)

 

[lolcakes52]

this conic is a hyperbola branching sideways i.e. x^2 is positive
therefore the focus is S(+-ae,0)
i think where you got lost is assuming that S could only be +ae, when it could actually be -ae as well since the question doesn't specify that S is +ae and S' is -ae [i.e. it could be that S is +ae and S' is -ae instead]
as a result, you end up with 2 possible solutions for PS' if PS=8, one where S(+ae,0) S'(-ae,0) or one where S(-ae,0) S'(+ae,0)

I concur. Well said.