Straight Line and Pair of Straight Lines 1 Question 62

62. One of the diameters of the circle circumscribing the rectangle ABCD4y=x+7. If A and B are the points (3,4) and (5,4) respectively, then find the area of rectangle.

(1985, 3M)

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Solution:

  1. Let O be the centre of circle and M be mid-point of AB.

Then, OMABM(1,4)

Since, slope of AB=0

Equation of straight line MO is x=1 and equation of diameter is 4y=x+7.

Centre is (1,2). Also, O is mid-point of BD

α+52,β+42=(1,2)α=3,β=0

AD=(3+3)2+(40)2=4

and AB=64+0=8

Thus, area of rectangle =8×4=32 sq units



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