Find the center and the radius of the circle.
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A)(6, -4), r = 36
B)(-6, 4), r = 6
C)(4, -6), r = 6
D)(-4, 6), r = 36

Question

Find the center and the radius of the circle.
-
A)(6, -4), r = 36 
B)(-6, 4), r = 6 
C)(4, -6), r = 6 
D)(-4, 6), r = 36

Quizplus · Accepted Answer

The coordinates of the center can be found by comparing the equation of the circle to standard form: 
(x - h)^2 + (y - k)^2 = r^2 
Thus, we have (x - 4)^2 + (y + 6)^2 = 6^2. 
Comparing this to standard form, we see that the center is at (4, -6) and the radius is 6. Therefore, the correct answer is choice C. The center can be found by looking at the coordinates of the point in the middle of the circle. From the diagram, the point in the middle is (4,-6). This means that the center of the circle is at (4,-6). 
To find the radius, we need to measure the distance from the center to any point on the circle. One way to do this is to use the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the distance from the center to any point on the circle, and a and b are the distances in the x and y directions, respectively, from the center to that point.

We can see from the diagram that one of the points on the circle is (4,-12). The distance in the x direction from the center to this point is 0, and the distance in the y direction is 6 (because the y-coordinate of the center is -6 and the y-coordinate of the point is -12). So:

c^2 = 0^2 + 6^2 
c^2 = 36 
c = 6

Therefore, the radius of the circle is 6, and the center is located at (4,-6). The answer is choice C.

Find the Center and the Radius of the Circle