Ease Into Prep with an SAT^® Question of the Day

The question asks for the diameter, which is twice the radius. When the equation of a circle is in the form (x − h)² + (y − k)² = r², the r represents the length of the radius. The question gives the equation in general form, so you need to complete the square to put the equation into standard form. You already have an x² and a y² in the given equation and the coefficients of x and y are even, so completing the square is fairly straightforward-there are just a lot of steps. Start by grouping the x's and y's together. Then, take the coefficient of the x term and divide it by 2, square it, and add it to the two terms with x variables. Do the same with the y term. Remember to add these amounts to the other side of the equation as well. Then factor the perfect squares and simplify:
x² + y² + 8x − 20y = 28
x² + 8x + y² − 20y = 28
(x² + 8x + 16) + (y² − 20y + 100) = 28 + 16 + 100
(x + 4)² + (y − 10)² = 144
This equation tells you that r² is 144, which means that the radius is 12, and the diameter is twice that, or 24, which is (B).