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  • The area of the circle, having a chord AB, A ≡ (5, 7) and B ≡ (7, 7), and a diameter along the line <img alt="\mathrm{10 x-2 y=58}" src="https://entrancecorne

The area of the circle, having a chord AB, A ≡ (5, 7) and B ≡ (7, 7), and a diameter along the line \mathrm{10 x-2 y=58}, is equal to

 

Option: 1

\pi


Option: 2

4\pi


Option: 3

58\pi


Option: 4

37\pi


Answers (1)

best_answer

The equation of  perpendicular bisector of the  chord AB is x = 6. The centre will be  the intersection point of x = 6 and 10x – 2y = 58 i.e.  centre ≡ ( 6,  1)

\mathrm{\begin{aligned} & \text { Hence radius }=\sqrt{(5-6)^2+(7-1)^2}=\sqrt{37} \\ & \text { Area }=37 \pi \end{aligned}}

 

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