Question

Please need help on this

Answer 1

Answer:

the center is (-4,7) and the radius is 3

Step-by-step explanation:

The center of a circle can be found using the equation $(x-h)^2 + (y-k)^2 = r^2$ and is (h,k) from it. Notice h and k are the opposite value as in the equation.  

First write the equation in this form.  

$x^2 + 8x + ( ?)+ y^2 - 14y + (?) + 56 = 0$  

Complete the square with each variable to find what numbers should go in place of the question marks.  

$(8/2)^2 = 4^2 = 16$  

$(-14/2)^2 = -7^2 = 49$  

Add 16 and 49 to both sides of the equation.  

$x^2 + 8x + 16 + y^2 - 14y + 49 + 56 = 16 + 49\\(x+4)^2 + (y-7)^2 + 56 = 65\\(x+4)^2 + (y-7)^2 = 9$  

So the center is (-4,7) and the radius is 3.