Verified answer

Completing the squares,

(x^2+8x+?) + (y^2-6y+?) = -8

(x^2+8x+16) + (y^2-6y+9) = -8 + 16 + 9

(x+4)^2 + (y-3)^2 = 17

Center: (-4, 3)

Radius = sqrt(17)

Hi,

Express the given equation as follows:

x^2 + y^2 + 8x - 6y + 8 = 0

=> (x)^2 + 2.x.4 + (4)^2 - 16 + y^2 - 2.y.3 + 3^2 - 9 + 8 = 0

=> (x + 4)^2 + (y - 3)^2 - 17 = 0

=> (x + 4)^2 + (y - 3)^2 = 17

=> (x + 4)^2 + (y - 3)^2 = [sqrt(17)]^2 ........... => (1)

Now compare the equation with general equation of a circle:

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

where (h , k) is the center and r is radius

So, we get (h , k) = (- 4, 3) and r = sqrt (17)

So the center of the circle is (- 4 , 3) and radius is sqrt(17)

Hope i helped u:)

to discover the equation quite often type, you pick for to end the sq. for the two x and y. (x^2 + 8x + sixteen) + (y^2 - 6y + 9) = sixteen + 9 (x + 4)^2 + (y - 3)^2 = 25 the middle is at (-4, 3) and the radius is 5

(x + 4 )^2 + ( y - 3)^2 = 17

so the radius is sqrt ( 17 )