Question

How do you find the radius of the circle: `x^2 + y^2 + 12x - 2y + 21 = 0`?

Answer 1

`r=4`

Explanation:

`x^2+y^2+D x+E y+F=0`
`C(a,b)" coordinates for center of circle"`
`a=-D/2" "b=-E/2" "F=21`
`x^2+y^2+12x-2y+21=0`
`D=12" "E=-2`
`a=-12/2=-6" "b=2/2=1`
`r=1/2 sqrt(D^2+E^2-4F)`
`r=1/2 sqrt(12^2+(-2)^2-4*21)`
`r=1/2sqrt(144+4-84)`
`r=1/2sqrt64" "r=1/2*8`
`r=4`