Question

What is the center and radius of the circle with equation (x - 5)2 + (y + 3)2 = 16?

A.) center (3, -5); radius = 4
B.)center (5, -3); radius = 4
C.)center (5, -3); radius = 16
D.)center (-5, 3); radius = 16

Answer 1

(x - 5)2 + (y + 3)2 = 16 should be written as (x - 5)^2 + (y + 3)^2 = 16.
Compare this to (x-h)^2 + (y-k)^2 = r^2. See that r^2 = 16? Then r = 4 units.

5 corresponds to h and -3 corresponds to k. Thus, B is correct.

Answer 2

center (5,-3), radius = 4

Explanation:

write the center and radius of the circle with equation

`(x - 5)^2 + (y + 3)^2 = 16`

Standard form of the circle is

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

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

now compare the given equation with standard form

`(x - 5)^2 + (y + 3)^2 = 16`

The value of h= 5 and k= -3 and r^2= 16

center (h,k) is (5,-3)

the value of
`r^2= 16`

Take square root on both sides

radius = 4