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Question
Obtain the equation of the circle for which (3, 4) and (2, -7) are the ends of a diameter.
Solution
The equation of a circle with (x1, y1) and (x2, y2) as end points of a diameter is
(x – x1)(x – x2) + (y – y1)(y – y2) = 0
Here the end points of a diameter are (3, 4) and (2, –7)
So equation of the circle is (x – 3)(x – 2) + (y – 4) (y + 7) = 0
x2 – 2x – 3x + 6 + y2 + 7y – 4y – 28 = 0
x2 + y2 – 5x + 3y – 22 = 0
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