Problem 65
Question
Give an example of a circle's equation in standard form. Describe how to find the center and radius for this circle.
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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 \(16\).
2Step 2: 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 \((3,4)\).
3Step 3: 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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