Question: If the line joining the points (1,2) and (3,6) is the diameter of a circle, find the equation of the circle.


Solution:
Given,

Let AB be the diameter of the circle. Given, coordinates of A (x1,y1) are (1,2) and coordinates of B (x2,y2) are (3,6).

Using formula of equation of circle when the coordinates of the diameter is given is,

(x - x1)(x - x2) + (y - y1)(y - y2) = 0

or, (x -1)(x -3) + (y -2)(y -6) = 0

or, x² -4x + 3 + y² - 8y + 12 = 0

or, x² + y² -4x -8y +15 = 0 is the required equation

Hence, the required equation of the given circle is x² + y² - 4x - 8y + 15 = 0.

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