Question

Find the area of the circle whose equation is x2+y2=6x-8y​

Answer 1

Given that the equation of a circle is :

`\green{ \boxed{\boxed{\begin{array}{cc} {x}^(2) + {y}^(2) = 6x - 8y \\ = > {x}^(2) + {y}^(2) - 6x + 8y = 0 \\ = > {x}^(2) + {y}^(2) + 2 * ( - 3) * x + 2 * 4 * y = 0 \\ \\ \sf \: standard \: equation \: o f \: circle \: is : \\ {x}^(2) + {x}^(2) + 2gx + 2fy + c = 0 \\ \\ \sf \: by \: comparing \\ \\ g = - 3 \\ f = 4 \\ c = 0 \\ \\ \sf \: radius \: \: r = \sqrt{ {g}^(2) + {f}^(2) - c } \\ = \sqrt{ {( - 3)}^(2) + {4}^(2) - 0 } \\ = √(9 + 16) \\ = √(25) \\ = 5 \: unit \\ \\ \bf \: area \: = \pi {r}^(2) \\ = \pi * {5}^(2) \\ =\pink{ 25\pi \: { unit }^(2) }\end{array}}}}`