let the point be (x,y)
(√(x^2 + y^2) = 2√(x-3)^2 + y^2) = 0
square both sides
x^2 + y^2 = 4(x^2 - 6x + 9) + y^2)
x^2 + y^2 = 4x^2 - 24x + 36 + 4y^2
3x^2 + 3y^2 - 24x + 36 = 0
x^2 + y^2 - 8x + 12 = 0
complete the square
x^2 - 8x + 16 + y^2 = -12 + 16
(x - 4)^2 + y^2 = 4
indeed a circle with centre (4,0) and radius 2
a point moves so that its distance from the origin is twice its distance from the point (3,0) show that the locus is a circle and find its centre and radius
1 answer
1 answer