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Chapter 2: Problem 69

Use a graphing utility to graph each circle whose equation is given. $$ (y+1)^{2}=36-(x-3)^{2} $$

Short Answer

Expert verified
The circle with the equation \((y+1)^{2}=36-(x-3)^{2}\) has the center at (-1, 3) and radius 6 units. The graph of this circle can be sketched using a graphing utility by first locating the center at (-1, 3) and then drawing a circle with radius 6 units from this center point.

Step by step solution

01

Identifying the Circle Parameters

The given equation can be identified as a circle equation. The general form of the equation of a circle is \((y-h)^{2} = r^{2} - (x-k)^{2}\). By comparing this with the given equation, we can identify that the center (h, k) is at the point (-1, 3) and the radius squared (\(r^{2}\)) is 36.
02

Calculating the Radius

Having the radius squared, we need to square root it to find the actual radius. Therefore, \(r = \sqrt{36} = 6\)
03

Graphing the Circle

For graphing, first locate the center of the circle at point (-1, 3). From the center, mark off the radius length (6 units) in all directions. Draw a circle that passes through all these marked points. This circle is the graph of the given circle equation.

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