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Find the coordinates of the midpoint of the chord cut by the circle x² + y² + 4x - 2y - 3 = 0 on the line y = x + 2.
- (-3/2, 1/2)
- (3/2, 1/2)
- (-3/2, -1/2)
- (3/2, -1/2)
Correct answer: (-3/2, 1/2)
Solution
The correct option is right because the midpoint of the chord can be found by substituting the line equation into the circle's equation, simplifying it, and then solving for the intersection points. The coordinates (-3/2, 1/2) accurately represent the midpoint of the chord formed by these intersections.
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