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Chapter 1: Problem 77

Find the center and radius of the circle. Then sketch the graph of the circle. $$x^{2}+y^{2}=25$$

Short Answer

Expert verified
The center of the circle is at the origin, \((0,0)\), and the radius of the circle is 5.

Step by step solution

01

Identifying the center

From the given equation, it can be that there are no \(h\) and \(k\) values. The equation is in the form \(x^{2} + y^{2}\). Therefore, the center of the circle is at the origin or \((0,0)\).
02

Calculating the radius

The given equation is \(x^{2} + y^{2} = 25\). The standard form for a circle's equation is \((x-h)^{2} + (y-k)^{2} = r^{2}\). So, here \(r^{2} = 25\), which means the radius \(r\) is \(\sqrt{25}= 5\).
03

Sketching the circle

To sketch the circle, first position the center at \((0,0)\) on a graph. Then, draw a circle around the center with a radius of 5. This will be accomplished by measuring 5 units out from the center in all directions.

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