Question

find the center and radius of the circle represented by the equation below, ((x + 9)^2 + (y - 8)^2 = 400)
answer attempt 1 out of a
center: (□,□)
radius: □
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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: Identify \(h\), \(k\), and \(r\) from the given equation

Given the equation \((x + 9)^2 + (y - 8)^2 = 400\), we can rewrite \(x + 9\) as \(x - (-9)\). So, comparing with the standard form:

• \(h = -9\) (from \(x - (-9)\))
• \(k = 8\) (from \(y - 8\))
• For the radius, we know that \(r^2 = 400\). Taking the square root of both sides, \(r=\sqrt{400}=20\) (we take the positive root since radius is a length).

Answer:

Center: \((-9, 8)\)
Radius: \(20\)