Problem 41
Question
Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$x^{2}+y^{2}=16$$
Step-by-Step Solution
Verified Answer
The center of the given circle is at the origin (0,0). The radius of the circle is 4 units. The domain and range of the given circle are both from -4 to 4.
1Step 1: Find the Center
Three is no constant term subtracted from x or y in the equation, so the center of the circle is at the origin point (0,0).
2Step 2: Determine the Radius
The equation of the circle is in the form \(x^{2}+y^{2}=r^{2}\), where r is the radius of the circle. Therefore, the radius r = \(\sqrt{16}\) = 4 units.
3Step 3: Graph the Circle
The graph of the circle can be drawn with radius 4 units and the center at origin. The circle touches the coordinates (4,0), (0,4), (-4,0) and (0,-4).
4Step 4: Identify Domain and Range
Once we have the graph, we can identify the domain and range. The domain (set of x-values) and range (set of y-values) of a circle's equation are defined by the radius. Therefore, the domain and range of this circle are from -4 to 4.
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Problem 40
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