Answer:
(3, -4) and r = 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 - 6x + ( ?)+ y^2 +8y + (?) + 16 = 0[/tex]
Complete the square with each variable to find what numbers should go in place of the question marks.
[tex](-6/2)^2 = -3^2 = 9[/tex]
[tex](8/2)^2 = 4^2 = 16[/tex]
Since 16 has already been added to the equation, just add 9 to both sides of the equation.
[tex]x^2 - 6x + 9 + y^2 +8y + 16 = 9\\(x-3)^2 + (y+4)^2 = 9[/tex]
So the center is (3,-4) and the radius is 3.
