Question

question
find the center and radius of the circle represented by the equation below.
$(x + 6)^{2}+(y + 8)^{2}=36$
answer attempt 1 out of 2
center: ( )
radius: i
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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 and \(r\) is the radius.

Step2: Rewrite the given equation to match the standard form

Given \((x + 6)^2+(y + 8)^2=36\), we can rewrite it as \((x-(- 6))^2+(y-(-8))^2 = 6^2\).

Step3: Identify the center and radius

Comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h=-6\), \(k = - 8\), and \(r = 6\).

Answer:

Center: \((-6,-8)\)
Radius: \(6\)