A and B are points in the plane such that PA/PB=K(constant) for all P on a circle Then value of - Maths - Conic Sections

Question

A and B are points in the plane such that PA/PB=K(constant) for all
P on a circle Then value of K cannot be equal to (A) 2 (B) 1 (C)1/2
(D)3/2

Rahul Raj · Accepted Answer

Dear student

Using the Apollonian Circles Theorem
Given two points A and B and a number r The locus of points P such
that AP/BP = r is a circle
But if r = 1, in this case it's the perpendicular bisector of
AB

so for question, if P lies on a circle, then K cannot be 1

Regards

A and B are points in the plane such that PA/PB=K(constant) for all P on a circle.Then value of K cannot be equal to (A) 2 (B) 1 (C)1/2 (D)3/2