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If two diameters of a circle lie along the lines x – y = 9 and x – 2y = 7, and the area of the circle is 38.5 sq cm, find the equation of the circle.

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The point of intersection of two diameters is the centre of the circle.

∴ point of intersection of two diameters x – y = 9 and x – 2y = 7 is (11, 2). 

∴ centre = (11, 2) 

Area of a circle = πr2

38.5 = πr2

⇒ r2 = \(\frac{38.5}{\pi}\)

⇒ r2 = 12.25 sq.cm 

the equation of the circle is: 

(x - h)2 + (y - k)2 = r2 

Where, (h, k) is the centre of the circle. 

r is the radius of the circle. 

⇒ (x - 11)2 + (y - 2)2 = 12.25 

(x - 11)2 + (y - 2)2 = 12.25

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