Math, asked by ns003132, 4 months ago

the center and radius of the circle given by x2+y2-4x-5=0​

Answers

Answered by pulakmath007
2

SOLUTION :-

TO DETERMINE :-

The center and radius of the circle given by

 \sf{ {x}^{2} +  {y}^{2} - 4x - 5 = 0  }

FORMULA TO BE IMPLEMENTED :-

For the circle of the form

 \sf{ {(x - a)}^{2}  +  {(y - b)}^{2}  =  {r}^{2} }

The center of the circle is ( a, b ) and

radius of the circle is r unit

EVALUATION :-

Here the given equation of the circle is

 \sf{ {x}^{2} +  {y}^{2} - 4x - 5 = 0  }

Which can be rewritten as below

 \sf{ {x}^{2}  - 4x + 4+  {y}^{2} - 9= 0  }

 \implies \:  \sf{ {x}^{2}  - 2.2.x +  {(2)}^{2} +  {y}^{2} = 9  }

 \implies \:  \sf{ {(x - 2)}^{2}  +  {(y - 0)}^{2} =  {(3)}^{2}   }

Which is of the form

 \sf{ {(x - a)}^{2}  +  {(y - b)}^{2}  =  {r}^{2} }

Hence the required center of the circle is ( 2, 0) and radius of the circle is 3 unit

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