Theory question 104
Coordinate GeometryThe line 2y = x + 3 meets the circle x2 + y2 − 2x + 6y − 15 = 0 at point M and N, where N is in the first quadrant. Find the coordinates of M and N.
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Model answer
Substitute x = 2y − 3: (2y − 3)² + y² − 2(2y − 3) + 6y − 15 = 0.
5y² − 10y = 0, so y = 0 or y = 2.
y = 0: x = −3; y = 2: x = 1.
N = (1, 2) (first quadrant), M = (−3, 0).
Explanation
Solve the line and circle simultaneously.