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Chapter 2: Problem 83

Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$x^{2}+y^{2}=25$$

Short Answer

Expert verified
The circle, as per the given equation \(x^{2}+y^{2}=25\), is centered at the origin. The circle has a radius of 5 units. With a square viewing window set from -6 to 6 on both axes, the complete circle can be seen.

Step by step solution

01

Understand the circle equation

The equation for a circle centered at the origin is \(x^{2} + y^{2} = r^{2}\), where \(r\) is the radius of the circle. For the given equation \(x^{2} + y^{2} = 25\), it can be easily seen that \(r^{2} = 25\). Therefore, the radius \(r\) of the circle is \( \sqrt{25} = 5\). This circle is centered at the origin (0,0) and has a radius of 5.
02

Choose the correct window size

In order to graphically show the entire circle with radius 5, make sure the window size includes values from -6 to 6 on both x and y axes. This will ensure the complete circle gets plotted within the viewing window.
03

Graph the circle

Input the equation \(x^{2} + y^{2} = 25\) in the graphing utility while setting the window size from -6 to 6 on both x and y axes. This will plot the circle centered at the origin with a radius of 5 units.

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