Circle graphs, quick question?

Question

im not sure how to read circle graphs

i know that (x-h)^2 + (y-k)^2 = r^2

where h,k is the coordinate of the center and r is the radius

but what if they gave u a question like

x^2 + y^2 +6x -4y + 3 = 0

how would u find the center and its radius?

Answer 1

convert it to the form

(x-h)^2 + (y-k)^2 = r^2

how

x^2 + y^2 +6x -4y + 3 = 0

collect x terms together and so y as well

(x^2+6x) + (y^2 - 4y) + 3 = 0

complete square in each part remembering to subtract what we add

(x^2+6x+9) + (y^2 - 4y+4) + 3-9 - 4 = 0

(x+3)^2 + (y-2)^2 - 10 = 0

take 13 to right

(x+3)^2 + (y-2)^2 =10 =(sqrt(10))^2

now it is above form center is (-3,2) radius sqrt(10)