The equation of a circular area rug is (x-4) ^2 + (y-1) ^2=16. Find the diameter and center of the rug

A. C (-1,-4)

d=4

B. C (1,4)

d=8

C. C (4,1)

d=4

D. C (4,1)

d=8

D. C (4,1)

d=8

Step-by-step explanation:

(x-4) ^2 + (y-1) ^2=16

This is of the form

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

The center is (h, k) and r is the radius

(x-4) ^2 + (y-1) ^2=4^2

The center is

(4,1) and the radius is 4

The diameter is 2 times the radius

d = 2*4 = 8

(x-4) ^2 + (y-1) ^2=16

The form of a circle is written as:

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

Where r is the radius h is the X-offset from the origin and k is the y offset from the origin.

In the given formula r = 4 (4^2 = 16)

h = 4

k = 1

The center of the circle is (h, k) = (4,1)

The answer is:

D. C (4,1)

d=8