The equation of a circle is given below.

x^{2}+(y+4)^{2} = 64x

2

+(y+4)

2

=64x, squared, plus, left parenthesis, y, plus, 4, right parenthesis, squared, equals, 64

What is its center?

((left parenthesis

4

,,comma

9

))right parenthesis

What is its radius?

If necessary, round your answer to two decimal places.

Given:

The equation of the circle is

We need to determine the center and radius of the circle.

Center:

The general form of the equation of the circle is

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

Let us compare the general form of the equation of the circle with the given equation to determine the center.

The given equation can be written as,

Comparing the two equations, we get;

(h,k) = (0,-4)

Therefore, the center of the circle is (0,-4)

Radius:

Let us compare the general form of the equation of the circle with the given equation to determine the radius.

Hence, the given equation can be written as,

Comparing the two equation, we get;

Thus, the radius of the circle is 8

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

c. 1,233 miles