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kramer
2 years ago
10

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

Mathematics
1 answer:
Semenov [28]2 years ago
6 0

Answer:

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 \times ( - 3) \times x + 2 \times 4 \times 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  }  \\  =  \sqrt{9 + 16}  \\   = \sqrt{25}  \\  = 5 \: unit \\  \\  \bf \: area \:  = \pi {r}^{2}  \\  = \pi \times  {5}^{2}  \\  =\pink{ 25\pi \:  { unit }^{2} }\end{array}}}}

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