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One of the diameters of the circle circumscribing the rectangle ABCD is 4y = x + 7. If A and B are the points (-3, 4) and (5, 4), respectively, then the area of the rectangle in square units is

(A)  22

(B)  32

(C)  42

(D)  26

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Correct option  (B)  32

Explanation :

See Fig.  Let M be the midpoint of AB so that M = (1, 4). Clearly, A and B do not lie on the  on the diameter 4y − x − 7 = 0. If O is the centre of the circle, then we know that

AD = 2(OM)   ...(1)

Since (bar)AB  is a horizontal line,(bar) OM is a vertical line and hence the equation of (bar)OM  is x = 1. Therefore, the line OM and the diameter intersect at O and we have O = (1,2).

Now  AD = 2(OM) = 2(2) = 4

 By hypothesis, AB is 8. Thus, the area of the rectangle ABCD = 8 x 4 = 32.

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