Question

Show a graph of two circles, the first circle with a center of (0,0) and a radius of 5 and the second circle with a center of (10,10) and a 3-unit radius.

Will give 50 PTS!!!

Answer 1

x² + y² = 25

(x - 10)² + (y - 10)² = 9

Explanation:

We can write out the equation of a circle based on the center and radius.

Equation of a Circle

The format for the equation of a circle is as follows:

• (x - h)² + (y - k)² = r²

In this equation, h is the x-coordinate of the center, k is the y-coordinate of the center, and r is the radius. So, we already have all the information we need to write out the equations. We can just plug in the information we were given.

The equation of the first circle is: x² + y² = 25.

The equation of the second circle is: (x - 10)² + (y - 10)² = 9.

Graphing the Circles

There are 2 possible ways the graph the circle. One possible way is to use the equation to find coordinate points on the circle and create a table.

However, I prefer to just use the radius and center. First, graph the center. Then, directly above, below, to the left, and to the right count out the radius. For example, for the first circle, I would graph a point at (0,0) and then count out 5 units to each side. Finally, connect the four points with a circle.

Below is a picture of both circles.