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## Homework Statement

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.

## Homework Equations

## 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]

BP.PB'= [itex]x^2-b^2+y^2[/itex]

So

[itex]a^2=b^2[/itex]

This result sugests that their is no constraint on P. This is not consistent with the question.

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