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

Let the equation of the circle bex2+y2+2gx+2fy+c=0This passes through (- 3, 4) and (5, 4).∴    −6g+8f+c+25=0 and, 10g+8f+c+41=0Subtracting (ii) from (i), we get g = -1. Since the centre (- g, - f) lies on 4 y = x + 7∴ −4f=−g+7⇒So, centre of the circle is at (1, 2)Now, AD = 2 GM=> AD = 2 (Length of the .l from G on AB whose eqn. is⇒ AD=2×2=4 Also, AB=8Hence, area of rectangle ABCD =c 4 x 8 = 32 sq. units.