Alg6.21

Find the equation of the locus of points which are equidistant from $A(-3,2),B(0,4)\,$

Let P(x,y) be a point in the locus.Then,the geometric condition is

$AP=BP\,$

$AP^{2}=BP^{2}\,$

$(x+3)^2+(y-2)^2=x^2+(y-4)^2\,$

$x^2+9+6x+y^2+4-4y=x^2+y^2-8y+16\,$

$6x-4y+13+8y-16=0\,$

$6x+4y=3\,$

Hence the equation of the locus is 6x+4y=3\,</math>