Question Detail
Question
The point (2,3) lies on the circle x² + y² + 4x - 2y - 15 = 0 at one end of a diameter. Find the coordinates of the other end.
Correct Answer
Option D is the correct answer.
Detailed Explanation
First verify (2,3) is on circle: 4+9+8-6-15=0, yes. Complete square: (x²+4x+4) + (y²-2y+1) = 15+4+1=20 → (x+2)² + (y-1)² = 20. Center = (-2,1). If (2,3) is one end of diameter, the other end is the reflection across center: (2×(-2)-2, 2×1-3) = (-4-2, 2-3) = (-6, -1).
Hint
The center is the midpoint of the diameter.