Question Detail
Question
Find the centre of the circle 4x² + 4y² - 12x - 20y + 9 = 0 after it has been simplified.
Correct Answer
Option D is the correct answer.
Detailed Explanation
Dividing the equation by 4 yields x² + y² - 3x - 5y + 9/4 = 0. Comparing with x² + y² + 2gx + 2fy + c = 0 gives 2g = -3 so g = -3/2, and 2f = -5 so f = -5/2. The centre is (-g, -f) = (3/2, 5/2).
Hint
First divide the equation by 4 to make the coefficients of x² and y² equal to 1.