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