Explanation:Equation of a circle is \((x-h)^2 + (y-k)^2 = r^2\)
Where, \((h, k)\) are the coordinates of the centre and \(r\) is the radius
\(x^2 + y^2 - 6x + 8y = 56\)
\(x^2 - 6x + y^2 + 8y = 56\)
\(x^2 + 9 - 6x + y^2 + 16+ 8y = 56 + 9 + 16\)
\((x-3)^2 + (y+4)^2 = 81\)
Therefore, Centre \(= (3, -4)\) and \(r = 9\)
Area = \(81π\)
Hence, option B
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I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/