#### 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 Option 1) Option 2) Option 3) Option 4)

As we learnt in

Circumcentre -

The point of intersection of the perpendicular bisectors of the sides of a triangle.

- wherein

The centre of the circumcircle of a triangle.

Let x be (h,k)

A,B, C lie on locus of x.

given that

Centre is

Circumstance is

Option 1)

This option is correct.

Option 2)

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

This option is incorrect.