One of the diameters of the circle circumscribing the rectangle ABCD is `4y=x+y`. If `A and B` are the points `(-3, 4) and (5, 4)` respectively, find the area of the rectangle and equation of the circle.

Explanation

Clearly, the centre of the circle lies on the line `4 y=x+7`.

The circle passes through `A(-3,4)` and `B(5,4)`.

The slope of the segment joining `A` and `B` is zero.

Therefore, the slope of the perpendicular bisector of `A B` is not defined.

Hence, the perpendicular bisector of AB will be parallel to the `y`-axis and will pass through `(frac{-3+5}{2}, frac{4+4}{2})=(1,4)`

The equation of the perpendicular bisector is `x=1`

The intersection point of the perpendicular bisector and `4 y=x+7` is `(1,2)`

`therefore` Centre `=(1,2)`

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