This question is from an SAT Math section. To correctly solve the answer, you must complete the square. This is a pretty difficult question for most students as they have never completed the square.
First, align the equation appropriately by keeping the x's together and the y's together.
X^2 + 20x + ______ + Y^2 + 16y + _______ = -20.
Then take half of each middle value (20 and 16) and square them. So half of 20 is 10. 10 squared is 100. That goes in the first space. Since you add 100 to the left side of the equation, you must add 100 to the right side of the equation. Then take half of 16 which is 8 and square 8 to get 64. So, in the second space put 64 but make sure you add it to both sides of the equation.
X^2 + 20x + 100 + Y^2 + 16y + 64 = -20 + 100 + 64
Now factor the x's and the y's into perfect squares.
So (x+10)2 + (y+8)2 = 144, which is the equation of a circle. (Notice the numbers used in the factoring are the original halfs of the middle number with the x and the y)
Remember the equation of a circle;
(x-h)2 + (y-k)2 = r2 which has center at (h,k) with a radius of r.
Therefore the center of the circle is (-10,-8). Notice that the numbers are additive inverses of the ones in the equation meaning opposite signs. Positive 10 in the equation gives a negative 10 as the x coordinate.
The center of the circle is (-10,-8) answer B
