Question

Prove that if the distance from a point (x, y) to the point (- 2, 0) is twice the distance from (x, y) to (4, 0) then (x, y) must lie on the circle with center (6, 0) and radius 4.

Answer 1

Step-by-step explanation:

(x + 2)² +;y²= 4(x – 4)²+4y²

or, x²+4x+4+;y² = 4x²–32x+64+4y²

or, 3x²+3y²–36x+60 = 0

or, x²+y²–12x+20=0

The above equation is the equation of circle centred at (6,0) of radius 4.