What is the value of a for the following circle in general form? x^2+y^2+ax+by+c=0

Lets' solve for:  
X^2 + y^2 + ax + by + c = 0

Step 1: Add -x^2 to both sides

ax + by + x^2 + y^2 + c + - x^2 = 0 + - x^2

ax + by + y^2 + c = - x^2

Step 2: Add - y^2 to both sides

ax + by + y^2 + c +  - y^2 = - x^2 + y^2

ax + by + c = - x^2 - y^2

Step 3: Add - by to both sides

ax + by + c + by = - x^2 - y^2 +  - by

ax + c = - by - x^2 - y^2

Step 4: Add - c to both sides

ax + c + - c = by - x^2 - y^2 +  - c

ax = - by - x^2 - y^2 - c

Step 5: Divide both sides by x.

ax/x = - by - x^2 - y^2 - c/ x

a = - by - x^2 - y^2 - c/x

Answer is:

a = - by - x^2 - y^2 - c/x

Answer 2: 

This circle has a radius of [0 – (–6)]/2 = 3 and is centered at (–2, –3). Drawing a diagram is helpful for getting a grasp on this.

The standard equation for a circle is (x – h)^2 + (y – k)^2 = f^2, where h is the x-coordinate of the center, k is the y-coordinate, and r is the radius length. Substituting our values, the standard equation is:

(x + 2)^2 + (y + 3)^2 = 9

Now expand the squared binomials and reorder the terms to match the specified form:

(x + 2)^2 + (y + 3)^2 = 9
x^2 + 4x + 4 + y^2 + 6y + 9 = 9
x^2 + y^2 + 4x + 6y = 0

And there you go!

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