Question

Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( –1, 0) is equal to 1/3. Then the circumcentre of the triangle ABC is at the point

Answer 1

(a) : Let P be a general point (x, y) such that

The locus is a circle with centre (5/4, 0)
As points A, B, C lie on this circle, the circumcentre of triangle ABC is (5/4, 0).