Problem 68 - College Algebra

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: Prepare to Graph the Circle

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

Step 3: 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.

Step 4: 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.