Alg6.20

Find the equation of the locus of points which are 5 units away from A(4,-3).

$A(4,-3)\,$ is a fixed point.

Let P(x,y) be a point in the given locus.

The geometric condition satisfied by P is

$AP=5\,$

$\sqrt{(x-4)^2+(y+3)^2}=5\,$

Squaring on both sides,

$x^2+16-8x+y^2+6y+9=25\,$

$x^2+y^2-8x+6y=0\,$