Question

23) Find the center of the circle

Answer 1

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 .