# F5 Maths chp.9 locus

A and B are two fixed points. If the locus of a moving point P is formed by the centres of all the circles passing through both points A and B, sketch and describe the locus of B.

Ans: the perpendicular bisector of AB

Rating

I cannot draw with limited tools but I can explain here. Please use some imagination to get my answers.

First, you put two points A and B differed by 10 cm horizontally ( for convenience only ).

If P is the centre of the circle and this circle passes through A and B at the same time, we must have PA = PB ( Radii ). It means APB is an isosceles triangle.

With the help of Form 2 concept about Isosceles Triangle, we know if we fix PA = PB of varied length, then P is moving in a vertical line which passes through the mid-point of AB ( P lies on the mid-point of AB in the case when P is the centre of the circle with diameter AB ).

In such a case, the vertical line is perpendicular to AB and must pass through their mid-points, which concludes the locus of P must be the perpendicular bisector of AB.