Question

Find the centre and radius of the circle x² + y²-12x + 6y +45-0
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Answer 1

An circle with radius 3√5, and centre (−6,3)

Explanation:

We have:

x2+y2+12x−6y=0

First we can collect "like" terms:

{x2+12x}+{y2−6}=0

Next we complete the square independently on the x and y terms

∴{(x+6)2−62}+{(y−3)2−32}=0

∴(x+6)2−36+(y−3)2−9=0

∴(x+6)2+(y−3)2=36+9

∴(x+6)2+(y−3)2=45

∴(x+6)2+(y−3)2=(3√5)2

And as such, we can identify the conic as an circle with radius 3√