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Geometry: Equation of a Circle
A circle with centre ( –5, –8) passing through ( –3, –8) has equation
x2 + x + y2 + y + = 0

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Worked Solution:

The circle with centre at ( 0, 0 ) and radius r has equation x2 + y2 = r2.
Replacing x by x – (–5) and y by y – (–8) moves the centre to ( –5, –8):
(x + 5)2 + (y + 8)2 = r2
The radius, r, is the distance between the centre and a point on the circle,
found using Pythagoras' Theorem: r2 = ((–3) – (–5))2 + ((–8) – (–8))2 = 22 = 4

The equation (x + 5)2 + (y + 8)2 = 4 expands to x2 + 10 x + y2 + 16 y + 85 = 0

© MEI Produced by Dr Ron Knott, revised 3 April 2007
tom . button [AT] mei . org . uk 		Test reference: GeomCircleEqun.html?ref=90222,qu=findequn