Question

the equation below describes a circle. what are the coordinates of the center of the circle?
$(x - 6)^{2}+(y + 5)^{2}=15^{2}$
a. $(-6,5)$
b. $(-6,-5)$
c. $(6,-5)$
d. $(6,5)$

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

Given \((x - 6)^2+(y+5)^2 = 15^2\), we can rewrite \(y + 5\) as \(y-(-5)\).

Step3: Identify the center coordinates

Comparing \((x - 6)^2+(y-(-5))^2 = 15^2\) with \((x - h)^2+(y - k)^2 = r^2\), we get \(h = 6\) and \(k=-5\). So the center is \((6,-5)\).

Answer:

C. (6, -5)