Question

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

Answer 1

D. C(4,1)

d=8

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

Answer 2

(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