Answer:
the center is (2,4) and the radius is 4
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 - 4x + ( ?)+ y^2 - 8y + (?) + 5 = 0[/tex]
Complete the square with each variable to find what numbers should go in place of the question marks.
[tex](-4/2)^2 = -2^2 = 4[/tex]
[tex](-8/2)^2 = -4^2 = 16[/tex]
Add 4 and 16 to both sides of the equation.
[tex]x^2 - 4x + 4 + y^2 - 8y + 16 + 4 = 4 + 16\\(x-2)^2 + (y-4)^2 + 4 = 20\\(x-2)^2 + (y-4)^2 = 16[/tex]
So the center is (2,4) and the radius is 4.
