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Chapter 1: Problem 78

Find the center and radius of the circle. Then sketch the graph of the circle. $$x^{2}+y^{2}=16$$

Short Answer

Expert verified
The center of the circle is at the origin (0,0) and the radius is 4 units. The sketch of the graph should be a circle centered at the origin with a radius of 4 units.

Step by step solution

01

Identify the centre and radius from the equation

Here, the equation of the circle is given as \(x^{2} + y^{2} = 16\). This equation can be written in the form \(x^{2} + y^{2} = r^{2}\) which is the standard form of a circle with centre at the origin (0,0). Here, the squared radius \(r^{2}\) is given as 16. To find the radius, take the square root of 16. Hence, the radius r is 4.
02

Identifying the Center

Since there is no number to adjust the x or y in the provided equation, this circle is centered at the origin, (0, 0).
03

Sketching the graph

On a graphing paper or graphing tool, plot the centre at the origin. Then, from the origin, draw a circle with a radius of 4 units. Make sure the circle is as round as possible and its boundary is 4 units away from the center in all directions.

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