A point moves in a plane so that its distances PA and PB from two fixed points A and B in the plane satisfy the relation PA-PB=k(k≠0),then the locus of P is
a hyperbola
Let(x,y) be any point on the hyperbola
x2a2−y2b2=1
By definition ,we have:
PA=e(x−ac)=ex−a
and PB =e(x+ac)=ax+a
∴PB−PA=(ex+a)−(ex−a)
=2a=k