A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times its distance from the point B(2,-1). Determine the equation of the curve.

Question

btaylor · Answer

@myininaya @Carl_Pham help? I know the answer, just not how to get it!

anonymous · Answer

Use the distance formula.
$$PA = 3 PB$$
$$(PA)^2 = 9 (PB)^2$$
$$(x-x_A)^2 + (y-y_A)^2 = 9 \{ (x - x_B)^2 + (y - y_B)^2 \}$$
$$(x+1)^2 + (y-1)^2 = 9 \{ (x - 2)^2 + (y+1)^2 \} $$
Reduce from there.  You'll get some kind of conic section, an ellipse I think.

btaylor · Answer

its a circle. thanx