Who is asking: Student
Level: Secondary

Question:

a)Find the equation of the locus of the point P which moves so that its distance from A(1,2) is always three times its distance from B(5,6)

b) Show that this locus is a circle and states the coordinates of its centre and the length of its radius

A point (x,y) is on the locus if and only if its distance to (1,2) is 3 times its distance to (5,6), that is

distance((x,y),(1,2)) = 3 distance((x,y),(5,6))

If you use the distance formula to find the distances above you get

sqrt((x - 1)² + (y - 2)²) = 3 sqrt((x - 5)² + (y - 6)²)

If you still have difficulties completing the problem tell us what you got and where you got stuck.