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.
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 = 
r2
38.5 = 
r2
⇒ 
⇒ 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
Ans: (x - 11)2 + (y - 2)2 = 12.25
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