Question

find the center and radius of the circle represented by the equation below.
$(x + 2)^2 + (y - 1)^2 = 100$
answer attempt 1 out of 2
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 \(h\) and \(k\) from the given equation

Given the equation \((x + 2)^2 + (y - 1)^2 = 100\), we can rewrite \((x + 2)^2\) as \((x - (-2))^2\). So, comparing with the standard form, \(h = -2\) and \(k = 1\).

Step3: Find the radius

We know that \(r^2 = 100\). Taking the square root of both sides, \(r=\sqrt{100}=10\) (we take the positive root since radius is a length).

Answer:

Center: \((-2, 1)\)
Radius: \(10\)