Question

find the center and radius of the circle x^2 - 6x + y^2 - 4y + 4 = 0

Answer 1

Complete the square on the x^2-6x part and factor the y^2-4y+4 part.

Answer 2

What do you get?

Answer 3

i know how to get the y^2 - 4y + 4 is (y-2)(y-2)

Answer 4

so that would be (y-2)^2

Answer 5

So now we have x^2-6x +(y-2)^2=0

Answer 6

Do you know how to complete the square?

Answer 7

i dont know how to complete the square of x^2 - 6x

Answer 8

Find the center of this circle
x^2-6x+y^2-4y+4=0
x^2-6x+9 + y^2-4y+4 = 9
(x-3)^2 + (y-2)^2 = 3^2

That's a circle of radius 3 with a center at (3,2)
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The other circle has the same center (concentric). Find its radius:
r^2 = 3^2 + 2^2
r^2 = 13
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--> (x-3)^2 + (y-2)^2 = 13
or, x^2-6x+y^2-4y=0