Introduction

Introduction

A circle is the set of all points in a plane that lie at one fixed distance from one fixed point. That fixed point is called the centre, and the fixed distance is called the radius of the circle.

What you already know. Before writing the circle's equation in coordinate form, this chapter reuses a few facts from earlier geometry and coordinate-geometry work:

• Standard properties of chords and tangents of a circle.
• The angle inscribed in a semicircle is always a right angle — this single fact is what lets one of the circle's equation forms be derived purely from the perpendicularity of two slopes.
• Two lines are perpendicular exactly when the product of their slopes is $-1$.
• Two lines are parallel exactly when their slopes are equal.

Combining these facts with the distance formula gives three different (but equivalent) ways to write down the equation of a circle, depending on what information a problem actually hands you — a centre and a radius, or the two endpoints of a diameter.