Question

Complete the square to find the center and radius of each circle.Show work please..x2+y2-6x+14y-6=0..And..x2+y2+8x+8y=0

Answer 1

center of circle is (3, -7) and the radius is 8

center of circle is (-4,-4) and the radius is
`5.66`

Explanation:

`x^(2) +y^(2) -6x +14y-6=0`

Rearrange the terms

`x^(2) -6x +y^(2) +14y-6=0`

Using the completing the square method

`(x-(6)/(2) )^(2) - ((6)/(2))^(2) + (y+(14)/(2) )^(2) - ((14)/(2))^(2) -6 =0`

Simplify,

`(x-(6)/(2) )^(2) + (y+(14)/(2) )^(2) =64`

`(x-3 )^(2) + (y+7 )^(2) =8^(2)`

Therefore the center of circle is (3, -7) and the radius is 8

Next example,

`x^(2) +y^(2)+8x+8y=0`

Rearrange the terms,

`x^(2) +8x+y^(2)+8y=0`

Using completing the square method,

`(x+(8)/(2) )^(2) - ((8)/(2))^(2) + (y+(8)/(2) )^(2) - ((8)/(2))^(2) =0`

Simplify,

`(x+4 )^(2) -16 + (y+4)^(2) -16 =0`

`(x+4 )^(2) + (y+4)^(2)= (4√(2))^(2)`

Therefore the center of circle is (-4,-4) and the radius is
`4√(2) =5.66`