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What is the area of the circle x^2 + y^2 - 4x - 2y = 14

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asicannot | Student, Kindergarten | (Level 2) eNoter

Posted December 1, 2012 at 5:56 AM via web

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What is the area of the circle x^2 + y^2 - 4x - 2y = 14

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted December 1, 2012 at 6:09 AM (Answer #1)

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The general notation of a circle having radius R and center (h,k) is given by;

`(x-h)^2+(y-k)^2 = R^2`

 

`x^2+y^2-4x-2y = 14`

`x^2-4x+y^2-2y = 14`

 

We know that;

`(x-a)^2 = x^2-2ax+a^2`

 

`x^2-4x+4-4+y^2-2y+1-1 = 14`

`x^2-4x+4+y^2-2y+1-4-1 = 14`

`(x-2)^2+(y-1)^2 = 14+5`

`(x-2)^2+(y-1)^2 = 19`

 

So R^2 = 19

 

Area of the circle = pi*R^2 = 22/7*19 = 59.71

 

Area of the circle is 59.71

 

 

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