3. The Circle


Also on this page:

General form of a Circle

slice

math expression


The circle with centre (0, 0) and radius r has the equation:

x2 + y2 = r2



math expression

The circle with centre (h, k) and radius r has the equation:

(x − h)2 + (y − k)2 = r2



Example 1

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Sketch the circle x2 + y2 = 4.


Answer


Example 2

Sketch the circle (x − 2)2 + (y − 3)2 = 16


Answer


Example 3

Sketch the circle (x + 4)2 + (y − 5)2 = 36


Answer


The General Form of the Circle

An equation which can be written in the following form (with constants D, E, F) represents a circle:

x2 + y2 + Dx + Ey + F = 0

This is called the general form of the circle.


This LiveMath document shows us both forms of the equation for a circle.

LIVEMath


Example:

Find the centre and radius of the circle

x2 + y2 + 8x + 6y = 0

Sketch the circle.


Answer


Exercises

1. Find the equation of the circle with centre (3/2, -2) and radius 5/2.


Answer


2. Determine the centre and radius and then sketch the circle:

3x2 + 3y2 − 12x + 4 = 0


Answer


3. Find the points of intersection of the circle

x2 + y2 − x − 3y = 0

with the line

y = x − 1.


Answer




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