a) What are the distances of the point(x,y) from (1,0) and (-1,0) respectively

Ans) I got this respectively.

But  for this im stuck.

b)Write down the equation of the locus of a point whose distance form (1,0) is TWICE its distance from (-1,0).

and

c)Show that the locus is a circle,and determine the center and radius.

Thnks in advance.

squaring on both sides, we get

(x-1)^2 + y^2 = 4 [(x+1)^2 + y^2] 

x^2 + y^2 - 2x + 1 = 4(x^2) + 4(y^2) + 8x + 4

3(x^2) + 3(y^2) + 10x + 3 = 0

x^2 + y^2 + (10/3)x + 1 = 0

comparing with standard form...

centre = (-5/3,0)

radius = rt[(5/3)^2 - 1] => rt[ 25/9 - 1] => rt(16/9] => 4/3 units...

Hope u got it...