Find the equation of set of all points P(x,y) that is twice as far from (-8,8) as from (-2,2).

Answer 1

Name your points A(-8,8) and B(-2,2)
So you want PA = 2PB

Use you distance between points formula:
√( (x+8)^2 + (y-8)^2 ) = 2√( (x+2)^2 + y-2)^2 )
square both sides

(x+8)^2 + (y-8)^2 = 4( (x+2)^2 + y-2)^2 )

I will leave it up to you to expand and simplify the equation