Question

what is the center of a circle represented by the equation $(x + 9)^2+(y - 6)^2 = 10^2$?
$(-9,6)$
$(-6,9)$
$(6,-9)$
$(9,-6)$

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Rewrite the given equation in the standard form

The given equation is \((x + 9)^2+(y - 6)^2=10^2\). We can rewrite \((x + 9)^2\) as \((x-(-9))^2\).

Step3: Identify the center \((h,k)\)

Comparing \((x-(-9))^2+(y - 6)^2=10^2\) with \((x - h)^2+(y - k)^2=r^2\), we get \(h=-9\) and \(k = 6\).

Answer:

\((-9,6)\) (i.e., the first option)