Find the center and radius of the circle.

Hello from MrBillDoesMath!

Center = (-4,3)

radius = 4

Discussion:

x^2 + y^2 + 8x -6y + 9 = 0

Let "complete the square" for the x and y terms:

x^2 + y^2 + 8x -6y + 9 = 0  =>                     group like terms

(x^2 + 8x ) + (y^2 - 6y) + 9 = 0 =>                complete the square for x, y

(x^2 + 8x + 16) + ( y^2 - 6y + 9) -16 - 9 +9 = 0  =>

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

(x+4)^2 + ( y-3)^2 = 16  =>

Therefore,

radius = sqrt(16) = 4,

Center = (-4,3)

Graph of function attached.

Thank you,

MrB

The nature of roots can help us to determine the answer to this question and discriminant can be used to determine the nature of the roots.

Discriminant = b² - 4ac

b = coefficient of x term = -9
a = coefficient of squared term = 4
c = constant term = 9

So, Discriminant = 81 - 4(4)(9) = -63

Since, the discriminant is negative, the equation will have complex zeros.This means its graph will not cross x-axis at any point.

So, the answer to this question is zero, option B