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

x^2 + y^2 + 6x - 8y + 21= 0.

Step-by-step explanation:

The center of this circle is (-3, 4) and the radius id 2.

So in Standard form, the equation is:

(x + 3)^2 + ( y - 4)^2 = 2^2

Converting to General form we have:

x^2 + 6x + 9  + y^2 - 8y + 16 = 4

x^2 + y^2 + 6x - 8y + 9 + 16 - 4 = 0

x^2 + y^2 + 6x - 8y + 21= 0.

i believe the answer is the polygon, heptagon.