Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
7. Circles in the Coordinate Plane
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Exercise 26 Page 580

Identify the center and the radius of each circle to write its equation.

Graph Equation
a. C
b. D
c. B
d. A
Practice makes perfect

We are asked to match each graph with its equation. First, let's recall the standard equation of a circle with the center at point (h,k) and a radius of r. (x-h)^2+(y-k)^2=r^2 Let's analyze each graph one at time.

Graph a.

First we will look at graph a and try to identify its center and radius.

Knowing that the center of the circle is ( -3, 0) and the radius is 2, we can write the equation.
(x-( -3))^2+(y- 0)^2= 2^2
â–Ľ
Simplify
(x+3)^2+(y-0)^2=2^2
(x+3)^2+y^2=2^2
(x+3)^2+y^2=4
This corresponds to equation C.

Graph b.

Next we will find the equation of graph b. Again, let's start with identifying the center and the radius of this circle.

Let's substitute the center of the circle ( 0, 3) and its radius 2 into the equation and simplify.
(x- 0)^2+(y- 3)^2= 2^2
â–Ľ
Simplify
x^2+(y-3)^2=2^2
x^2+(y-3)^2=4
Therefore graph b corresponds to equation D.

Graph c.

Now let's move to graph c. We will take a look at the graph to identify the center and the radius of the drawn circle.

Next we will substitute the center of the circle ( 3, 0) and its radius 2 into the circle equation and simplify.
(x- 3)^2+(y- 0)^2= 2^2
â–Ľ
Simplify
(x-3)^2+y^2=2^2
(x-3)^2+y^2=4
As we can see, graph c matches equation B.

Graph d.

Finally we will take a look at graph d. Let's identify the center and the radius of this circle.

Next we will substitute the center of the circle ( 0, -3) and its radius 2 into the circle equation and simplify.
(x- 0)^2+(y-( -3))^2= 2^2
â–Ľ
Simplify
(x-0)^2+(y+3)^2=2^2
x^2+(y+3)^2=2^2
x^2+(y+3)^2=4
We found that graph d matches equation A.