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Chapter 1: Problem 80

Find the center and radius of the circle. Then sketch the graph of the circle. $$x^{2}+(y-1)^{2}=1$$

Short Answer

Expert verified
The center of the circle is at point (0, 1) and the radius is 1. The graph is a circle centered at point (0, 1) with a radius of 1 unit.

Step by step solution

01

Identify the center of the circle

The center of the circle is given by the coordinates of the point (0, h) where h corresponds to the term subtracted from y in the equation. From the given equation \(x^{2}+(y-1)^{2}=1\), we can see that h = 1. Thus, the center of the circle is at the point (0, 1).
02

Determine the radius of the circle

The radius of the circle can be found by taking the square root of the number on the right side of the equation, which is given by \(r^{2}\). Here, from the equation \(x^{2}+(y-1)^{2}=1\), we can see that \(r^{2}\) = 1, thus the radius \(r = \sqrt{1} = 1\).
03

Sketch the graph of the circle

To sketch the graph, plot the center point (0,1) on the coordinate plane and then plot points 1 unit distance away in all directions to represent the radius of the circle. Connect these points to form a circle. The sketch will represent a circle centered at (0, 1) with a radius of 1.

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