3. The Circle
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The circle with centre (0, 0) and radius r has the
equation:
x2 + y2 = r2
The circle with centre (h, k) and radius r has the equation:
(x − h)2 + (y − k)2 = r2
Example 1
Need Graph Paper?
Sketch the circle x2 + y2 = 4.
Example 2
Sketch the circle (x − 2)2 + (y − 3)2 = 16
Example 3
Sketch the circle (x + 4)2 + (y − 5)2 = 36
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.
Example:
Find the centre and radius of the circle
x2 + y2 + 8x + 6y = 0
Sketch the circle.
Exercises
1. Find the equation of the circle with centre (3/2, -2) and radius 5/2.
2. Determine the centre and radius and then sketch the circle:
3x2 + 3y2 − 12x + 4 = 0
3. Find the points of intersection of the circle
x2 + y2 − x − 3y = 0
with the line
y = x − 1.
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