Question

Draw and describe the locus in each of the following cases:

(iv) The locus of centres of all circles passing through two fixed points.

Answer 1

Find the locus:

The locus of a point that is equidistant from two fixed points is the perpendicular bisector of the line segment connecting the two points.

Construct a circle with $O$ as center.

Take two points $A$ and $B$ on it and join them.

Since, the locus of a point that is equidistant from $A$ and $B$ is the perpendicular bisector of the line segment connecting the two points.

Thus, the locus of $O$ is the perpendicular bisector of the line segment connecting two points $A$ and $B$.

Hence, the locus of centers of all circles passing through two fixed points is the perpendicular bisector of the line segment connecting the two given points.