Correct option (B) 32
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.