I'm quite confused about what should I write about this problem. Is there anyone that could help me explain and answer this, please?
Suppose a classmate missed the lessons on completing the square to find the center and radius of a circle. Explain the process to them. If it helps, use a problem you’ve already done as an example.
x^2 + 4x + y^2 - 6y -12 = 0
Standard form of a circle with center (h,k) is (x-h)^2 + (y-k)^2 = r^2
we want to get the red equation into that form to find the center , (h,k)
x^2 + 4x + y^2 - 6y - 12 = 0 'complete the square ' for 'x' by taking 1/2 of the coefficient of x
then square it and add it to both sides of the equation to keep
x^2 + 4x + 4 + y^2 - 6y - 12 = 4 do the same thing for the 'y' of the equation
x^2 + 4x +4 + y^2 -6y +9 -12 = 4 + 9 Now reduce the x and y portions to squares of binomials
(x+2)^2 + (y-3)^2 -12 = 4 + 9 add 12 to both sides
(x+2)2 + (y-3)2 = 25
(x+2)2 + (y-3)2 = 52 Now you can readily see h,k as (-2,3) and the radius = 5