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23) Find the center of the circle

23) Find the center of the circle-example-1
User Saptarsi
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1 Answer

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Given Equation of Circle :-


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


\\

Solution:-

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


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

in which

  • coordinate of center = (-g , -f )
  • radius of circle =
    √(g^2+f^2-c)

Comparing given equation with general form of circle -

  • g = -5
  • f = 4
  • c = 1

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

➥ (5, -4)


\\

Also, radius of circle =
√((-5)^2+4^2-1)


√(25+16-1)


√(40)


2√(10) units .

User Dave Clements
by
7.4k points

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