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Chapter 2: Problem 68

Use a graphing utility to graph each circle whose equation is given. $$ x^{2}+y^{2}=25 $$

Short Answer

Expert verified
The plotted graph will feature a circle centered at the origin (0,0) with a radius of 5 units, effectively having the circumference touch the points at (5,0), (-5,0), (0,5) and (0,-5).

Step by step solution

01

Understand the Nature of The Circle

Examine the given equation \(x^{2} + y^{2} = 25\). This equation represents a circle where the x and y coordinates are centered around the origin (0,0), hence it is centered at (0,0). The radius is the square root of 25, which equals 5.
02

Prepare to Graph the Circle

Setup the graphing utility. Mark the origin (0,0) as it is the center of the circle.
03

Plot the Radius of the Circle

From the origin, measure 5 units in all directions (left, right, up, down) as this is the radius of the circle.
04

Draw The Circle

Use the graphing utility to draw the circle, ensuring that it is centered at (0,0) and its boundary is 5 units away from the center in all directions.

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