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 [tex](x-h)^2 + (y-k)^2 = r^2[/tex] 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.
[tex]x^2 + 8x + ( ?)+ y^2 - 14y + (?) + 56 = 0[/tex]
Complete the square with each variable to find what numbers should go in place of the question marks.
[tex](8/2)^2 = 4^2 = 16[/tex]
[tex](-14/2)^2 = -7^2 = 49[/tex]
Add 16 and 49 to both sides of the equation.
[tex]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[/tex]
So the center is (-4,7) and the radius is 3.
