A point P moves so that its distances from A(a, 0), A'(-a, 0), B(b, 0) B'(-b, 0) are related by the equation AP.PA'=BP.PB'. Show that the locus of P is a hyperbola and find the equations of its asymptotes.
The Attempt at a Solution
AP.PA' = [itex]((a-x)\boldsymbol i + y\boldsymbol j).((-a-x)\boldsymbol i+y\boldsymbol j)[/itex]
AP.PA' = [itex]x^2-a^2+y^2[/itex]
BP.PB' = [itex]((b-x)\boldsymbol i + y\boldsymbol j).((-b-x)\boldsymbol i+y\boldsymbol j)[/itex]
This result sugests that their is no constraint on P. This is not consistent with the question.