Question

what is the radius of a circle with an equation: x^2 + y^2 + 2x + 4y -9 = 0

Answer 1

do u know what is general form of a circle?

Answer 2

its \[x ^{2}+y ^{2}+2gx+2fy+c=0\]

Answer 3

use completing the square

--> (x^2 +2x) + (y^2 +4y) = 9

--> (x^2 +2x + 1) + (y^2 + 4y + 4) = 9 + 1+4

--> (x+1)^2 + (y+2)^2 = 14

r^2 = 14

Answer 4

(x^2 +2x) + (y^2 +4y) = 9


(x^2 +2x + 1) + (y^2 + 4y + 4) = 9 + 1+4

(x+1)^2 + (y+2)^2 = 14

r^2 = 14

Answer 5

in your problem g=1 and f=2 and c=-9
now rad\[\sqrt{g ^{2}+f ^{2}-c}=\sqrt{1+4+9}=\sqrt{14}\]ius=