Question

The equation of a circle is given below.

Answer 1

Answer:

(h,k) = (32,-4)

r = 32

Step-by-step explanation:

The general equation for a circle is given by:

$(x-h)^2+(y-k)^2=r^2$   (1)

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

You have the following equation:

$x^2+(y+4)^2=64x$   (2)

You first need to complete squares in order to obtain an equation of the form (1). Thus, you have that the second term must be in a perfect square trinomial:

2b = 64

b = 32

Then, you have to sum 32^2 and also subtract the same number in the expression (2):

$x^2-64x+(y+4)^2=0\\\\(x^2-64x+32^2)+(y+4)^2-32^2=0\\\\(x-32)^2+(y+4)^2=32^2$

you compare the last result with expression (1) and obtain that the raiuds of the circle is r = 32

Furthermore, the center of the circle is (h,k) = (32,-4)