Question

Determine the equation of the circle shown in the graph.

Answer 1

B.

Explanation:

The equation of a circle with center at (h, k) and radius r is

`(x - h)^2 + (y - k)^2 = r^2`

We have center at (-5, 0). That makes h = -5, and k = 0.

The radius is 3, so r = 3.

`(x - (-5))^2 + (y - 0)^2 = 3^2`

`(x + 5)^2 + y^2 = 9`

Answer: B.

Answer 2

B

Explanation:

The equation of a circle has the form:

`(x-h)^2+(y-k)^2=r^2`

Where (h, k) is the center of the circle and r is the radius.

From the graph, we can see that the center of the circle is at (-5, 0). So, (h, k) is (-5, 0), where h = -5 and k = 0.

And by counting, we can determine that the radius of the circle is three units. Hence, r = 3.

Substitute the information into the equation:

`(x-(-5))^2+(y-(0))^2=(3)^2`

Simplify. Therefore, our equation is:

`(x+5)^2+y^2=9`

Our answer is B.