If A=(-1,3) B=(2,7) P=(x,y). Derive an equation for the set C={P:|AP|=alpha|BP|} and show that it is a circle.

Question

I have tried the algebraic route but this is messy and believe there is a better way to do it such as through using the fact that the perpendicular bisectors of two chords meet at the centre however I am having difficulty getting there. 0

Answer 1

I get: $(x,y) \in C$ iff

$(x+1)^2+(y-3)^2=\alpha^2(x-2)^2+\alpha^2(y-7)^2$

For $\alpha=1$ we have: $C$ is a straight line and not a circle !!