one diameter of the circle circumscribing the rectangle ABCD is 4y=x+7.If the coordinates of A & B are (-3,4) &(5,4) respectively , find the equation of the circle.

Centre P of the circle lies on the line ...(1)

and perpendicular bisector of AB.

As AB is parallel to x-axis, therefore, perpendicular bisector of AB passes through and is parallel to y-axis. So, its equation is

 x = 1  ...(2)

On solving equations(1) and (2), we get

x = 1, y = 2.

Thus, the coordinates of centre P are (1, 2).

radius = AP =

Hence, the equation of the circle is

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