Respuesta :

Given Equation of Circle :-

[tex]\bull\:[/tex][tex]\sf{x^2+y^2 -10x+8y + 1= 0}[/tex]

[tex]\\[/tex]

Solution:-

The general form of circle is given by the equation by the equation -

[tex]\green{ \underline { \boxed{ \sf{x^2+y^2 + 2gx+2fy + c = 0}}}}[/tex]

in which

  • coordinate of center = (-g , -f )
  • radius of circle = [tex]\sqrt{g^2+f^2-c}[/tex]

Comparing given equation with general form of circle -

  • g = -5
  • f = 4
  • c = 1

So, Center of Circle = (-(-5), -4)

➥ (5, -4)

[tex]\\[/tex]

Also, radius of circle = [tex]\sqrt{(-5)^2+4^2-1}[/tex]

➥ [tex]\sqrt{25+16-1}[/tex]

➥ [tex]\sqrt{40}[/tex]

➥ [tex]2\sqrt{10}[/tex] units .

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