F5 Maths chp.9 locus

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.


Hope I can help you.