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

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

Let the coordinates of point A be (x, y).
Mid-point of AB is (2, - 3), which is the center of the circle.
image
⇒ x + 1 = 4 and y + 4 = -6

⇒ x = 3 and y = -10
Therefore, the coordinates of A are (3,-10).

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