This is a question the equation of a circle. explain your answer. picture provided.

Step-by-step explanation:

x^2 + y^2 + 8x - 8y + 24 = 0 should be rewritten in preparation for "completing the square:"  x^2 + 8x             + y^2 - 8y                + 24 = 0.

To complete the square of x^2 + 8x, take half of the coefficient (8) of the x term. Square this result (square 4), obtaining 16.  Add 16 and then immediately subtract 16:  you'll get x^2 + 8x + 16 - 16.

Doing the same thing with y^2 - 8y, you'll get:

                                                          y^2 - 8y + 16 - 16.

Putting this all back together:  from x^2 + y^2 + 8x - 8y + 24 = 0

you'll get   x^2 + 8x + 16 - 16 + y^2 - 8y + 16 - 16 + 24 = 0.

Note that the trinomial squares x^2 + 8x + 16 and y^2 - 8y + 16 can be rewritten as the squares of binomials:

                                                       (x + 4)^2 - 16 + (y - 4)^2 - 16 + 24 = 0.

Gathering the constant terms together on the right, we obtain:

                                                      (x + 4)^2  + (y - 4)^2  = 8.

comparing this result to                (x - h)^2 + (y - k)^2 = r^2,

we see that h = -4, k = 4 and r^2 = 8.

Statement A is incorrect; the radius is 2√2.

Statement B is correct; see A (above).

Statement C is incorrect (see "h = -4, k = 4" above)

Statement D is correct.