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Question:

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is the point (1, 4).

Solution:

Center of circle is the midpoint of the diameter.
Let A be (x, y).
Then 2 = (x + 1)/2, and -3 = (y + 4)/2.
Solving these equations, we get x = 3, and y = -10.
So, the coordinates of A are (3, -10).