The Family of Circles
Coordinate Geometry has been making its regular appearance in CAT and other MBA entrance exams. An important part of Coordinate Geometry is circles and at times the questions can get quite complicated if you don’t know some shorter ways of approaching it. An important and fundamental concept in circles is the family of circles. It helps to solve some very lengthy questions in a quick span of time. Trust me, its application is quite revolutionary. But what do we mean by the family of circles?
The family of circles is a set of circles with a common property. All these circles will exhibit a common property. For example, if we say that two circles intersect each other at two points A and B, then there can be an infinite number of circles that can pass through these two points as no unique circle can be drawn passing through two points. For a unique circle, we need it to pass through three points. Now all such circles that will pass through A and B will together be known as the family of circles. One by one we shall see some cases of the family of circles and how they are helpful.
I hope the application part of the concept, Family of Circles is clear now. Practice more and more such questions to get a better understanding of.