Question

1. The equation of a circle is (x + 4)2 + (y – 6)2 = 48

What is the center of the circle?

What is its radius (round to the nearest tenth)?

Answer 1

Center of circle = (-4,6)

Radius = 6.9

Explanation:

Formula of a circle:

`{(x - a)}^(2) + {(y - b)}^(2) = {c}^(2)`

Center of circle = (a, b)

Radius= c

Your question is:

`{(x + 4)}^(2) + {(y - 6)}^(2) = 48`

a= - 4 because - (-4) will only equal to 4

b= 6 because - (6) will only equal to - 6

If (a, b) is the center of the circle, thus (-4,6) is the center of the circle.

To find the radius.

If c = radius.

`{c}^(2) = 48 \\ c = √(48) \\ c = 4 √(3)`

`4 √(3) = 6.92820323`

Note: Please use a calculator when finding the radius.

Thus to the nearest tenth

c= 6.9

Thus the radius is 6.9