Question

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.

Answer 1

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

Answer 2

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.

Answer 3

its a circle. thanx