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Chapter 1: Problem 79

Find the center and radius of the circle. Then sketch the graph of the circle. $$(x-1)^{2}+(y+3)^{2}=9$$

Short Answer

Expert verified
The center of the circle is at the point (1, -3), and the radius of the circle is 3 units.

Step by step solution

01

Identifying the Center

The center is given by the values \(-h\) and \(-k\). Therefore, comparing the given equation \((x-1)^{2}+(y+3)^{2}=9\) with the standard equation of a circle, we get the center of the circle as \((1, -3)\).
02

Finding the Radius

The value of \(r^2\) is given on the right-hand side of the equation. Hence, the radius (\(r\)) of the circle is the square root of 9, which is 3.
03

Sketching the Circle

Plot the center at point \((1, -3)\). From there, draw a circle of radius 3 units. To ensure accuracy, plot points a distance of 3 units in all directions (up, down, left, and right) from the center and connect them in a circular shape.

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