# Co-ordinate Geometry of Circle

LCH Paper 2 Q1 The Circle

Xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

LCH Paper2 Q1 The Circle

LCHM 2008 II 1ci

2009 p2 q1a

2010 p2 q1 b2

2010 p2 q1 c
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Topic Overview

Co-ordinate geometry of the circle (or simply ‘The Circle’) is the second of the co-ordinate topics on our course. It is therefore assumed that students studying The Circle have an adequate working knowledge of the ideas from The Line, the first of the co-ordinate geometry topics. For example, it is taken for granted that students are familiar with the perpendicular distance formula, which is frequently used in The Circle, in connection with questions on tangents. It is also assumed that students are familiar with terms such as tangent and chord, and can recall some of the more elementary geometry theorems from Junior Certificate, e.g., that a radius perpendicular to a chord bisects that chord.

Questions on The Circle generally occur at two levels. At the more straightforward or superficial level, we have to know formulae, learn to recognise the need for them, and substitute values. At the deeper level, information has to be analysed and often a diagram drawn. Then a strategy has to be devised, which may involve four or more separate stages. In such questions, we tend to employ methods rather than relying on formulae.

Topic Structure

The study of Senior Cycle Co-ordinate Geometry of the Circle can be divided into the following sections:

1. Equation of a Circle

2. Two circles

3. Circle and Line

4. Two circles and a line