Question Detail

MTH 101 Analytical Geometry - The Circle Objective Question

Question

In the general equation of a circle x² + y² + 2gx + 2fy + c = 0, what are the coordinates of the centre?
Options
A (g, f)
B (-g, -f)
Correct Answer
C (2g, 2f)
D (-2g, -2f)
Correct Answer

Option B is the correct answer.

Detailed Explanation

By comparing the expanded standard form (x - a)² + (y - b)² = r² with the general form, we find that the centre (a, b) is equal to (-g, -f).

Hint

This is derived from completing the square on the general form.

Question Info