Question

determine the center and radius of the circle.
$(x + 6)^{2}+(y + 1)^{2}=100$
part 1 of 2
the center is $(square,square)$.
part 2 of 2
the radius is $r=square$.

Explanation:

Step1: Recall the standard circle equation

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

Step2: Rewrite the given equation

Given \((x + 6)^2+(y + 1)^2=100\), we can rewrite it as \((x-(-6))^2+(y - (-1))^2 = 10^2\).

Step3: Identify the center

Comparing with the standard form, \(h=-6\) and \(k = -1\), so the center is \((-6,-1)\).

Step4: Identify the radius

Since \(r^2=100\), then \(r=\sqrt{100}=10\).

Answer:

Part 1 of 2: The center is \((-6,-1)\).
Part 2 of 2: The radius is \(r = 10\).