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!
