Question

11.1: distance and midpoint formulas; circles
score: 16/24 answered: 14/18
question 15
give the center and radius of the circle. ((x + 2)^2 + (y - 4)^2 = 5)
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 is \((x + 2)^2+(y - 4)^2=5\). We can rewrite \((x + 2)^2\) as \((x-(- 2))^2\). So, comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h=-2\), \(k = 4\).

Step3: Find the radius

Since \(r^2 = 5\), then \(r=\sqrt{5}\) (we take the positive square root because radius is non - negative).

Answer:

Center: \((-2,4)\)
Radius: \(\sqrt{5}\)