Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units? a.) x^2+y^2+4x+6y-51=0 b.) x^2+y^2-4x-6y-51=0 c.) x^2+y^2+4x+6y-3=0 d.) x^2+y^2-4x-6y-3=0

First you need to use the standard form of a circle and then transform it into the general form of a circle.

Standard Form of a Circle.


To use the standard form of a circle, we need to know the center of the circle and the radius of the circle. Our center is at (-2, -3), which is (h, k). Our radius is half of the diameter, which the diameter is 8 so 8 / 2 = 4. So we have a radius of 4. 
In our Standard Form of a Circle, the h = -2 and the k = -3 and the 4 = r
Now we can turn this into the general form of a circle.

Insert our point (-2, -3) and our radius of 4 into the standard form of a circle equation and transform it into the general form.





Expand (x + 2)^2

Expand (y + 3)^2

Move the 16 over to the left side by adding a - 16


Now arrange and combine like terms

Gathering all constant values

Gathering all x and y values


Combining all constant terms


There is nothing else to combine so we have the general form of a circle, which is so the answer is C

C

The answer is a segment line