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Chapter 2: Problem 64

Give an example of a circle's equation in standard form. Describe how to find the center and radius for this circle.

Short Answer

Expert verified
The standard form of the given circle's equation is \((x-3)^2 + (y+4)^2 = 25\). The center of the circle is (3,-4) and the radius is 5.

Step by step solution

01

Provide an example of a circle's equation in standard form

Let's consider the equation \((x-3)^2 + (y+4)^2 = 25\) as an example of a circle's equation in standard form.
02

Identify the center of the circle

From the equation, note that the term with \(x\) is \((x-3)\) and the term with \(y\) is \((y+4)\). Comparing this with the standard form, we see that \(h=3\) and \(k=-4\). Thus, the center of the circle is \((3,-4)\).
03

Determine the radius of the circle

From the equation, the right side is equal to 25, which is the square of the radius. Comparing this with the standard form, we infer that \(r^2 = 25\). Taking the square root of both sides, we get \(r = 5\). Therefore, the radius of the circle is 5.

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