Write the equation of the circle in general form.
Show all of your work please.

  x^2 +y^2 -8x +4y +11 = 0

Step-by-step explanation:

The center of the given circle is located at (x, y) = (4, -2). Its radius is 3.

You know this because the center is halfway between the vertical and horizontal extremes, and the radius is half the difference of those extremes. You can determine this by counting squares, or "by eye," or by working with the coordinates of the extreme points.

For example, the horizontal extremes are (1, -2) and (7, -2). The diameter is the difference of the x-values: 7 -1 = 6, so the radius is 6/2 = 3. The x-coordinate of the center is (1+7)/2 = 4.

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The standard form of the equation of a circle is ...

  (x -h)^2 + (y -k)^2 = r^2

where (h, k) is the center, and r is the radius.

For this circle with center (4, -2) and radius 3, the standard form equation is ...

  (x -4)^2 + (y +2)^2 = 9

General form has the parentheses removed and the polynomial written in descending powers of the variables:

  x^2 -8x +16 +y^2 +4y +4 = 9

  x^2 +y^2 -8x +4y +11 = 0