Question

11.1: distance and midpoint formulas; circles
score: 18/24 answered: 15/18
question 16
give the center and radius of the circle. $(x + 1)^2 + (y - 1)^2 = 4$
center:
radius:
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Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle 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

The given equation \((x + 1)^2+(y - 1)^2 = 4\) can be rewritten as \((x-(- 1))^2+(y - 1)^2=2^2\).

• For the center: Comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h=-1\) and \(k = 1\). So the center is \((-1,1)\).
• For the radius: Since \(r^2 = 4\), then \(r=\sqrt{4}=2\).

Answer:

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