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Chapter 2: Problem 65

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 equation for the given circle is \( (x-3)^2 + (y-4)^2 = 16 \), its center at point \( (3,4) \) and radius equals to \(4\) units.

Step by step solution

01

Define a Circle Equation

First, let's define a circle equation in standard form, for example: \( (x-3)^2 + (y-4)^2 = 16 \). In this equation, \((h, k)\) are replaced by \((3, 4)\), respectively and \(r^2\) by \(16\).
02

Identifying the center

In standard form equation, the center of the circle is given by the point \((h, k)\). Hence, by looking at the equation, we can identify that the center of our circle is at point \((3,4)\).
03

Finding the radius

In standard form equation, the square of the radius is the constant on the right side of the equation. In our equation, 16 represents the square of the radius. Hence, the radius of the circle is equal to the square root of 16 which is \(4\) units.

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