Question

what coordinate pair is the center of the circle represented by $(x - 3)^2+(y + 4)^2 = 9$?
a $(-4,3)$
b $(-3,4)$
c $(3,-4)$
d $(4,-3)$

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle.

Step2: Rewrite the given equation

The given equation is \((x - 3)^2+(y+4)^2 = 9\), which can be rewritten as \((x - 3)^2+(y-(-4))^2=3^2\).

Step3: Identify the center coordinates

Comparing with the standard form \((x - h)^2+(y - k)^2=r^2\), we have \(h = 3\) and \(k=-4\).

Answer:

C. \((3,-4)\)