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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 find the area of the rectangle.<div class='qn

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 find the area of the rectangle.

Option: 1

8


Option: 2

16


Option: 3

32


Option: 4

48


Answers (1)

best_answer

Points A and B have the same y-co-ordinate 4. 

\therefore \mathrm{AB} \| \mathrm{OX} \text { (with equation } \mathrm{y}=4 \text { ). }

The mid-point of AB is E(1, 4)

Let F be the centre of the circle.   Then FE is perpendicular AB.

Since \mathrm{AB}\|\mathrm{OX}, \mathrm{FE}\| \mathrm{OY}    ∴ x-co-ordinate of F is 1.

Since F lies on 4y = x + 7, y-co-ordinate of F is 2

∴FE = 2 and consequently, l(CB) = 4.

But l(AB) = 8.

Hence area of rectangle ABCD is equal to 32 sq. units.

 

 

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