Find the centre and radius of the following circles : `4x^2 + 4y^2 - 4x + 12y - 15 = 0`

Explanation

`4x^2 + 4y^2 - 4x + 12y - 15 = 0`
or, `x^2 + y^2 -x + 3y - (15)/4 = 0`
`therefore` 2g = -1, 2f = 3, c = -15/4
`therefore` g = -1/2, f = 3/2
`therefore` Centre at (-g, -f) = (1/2, -3/2)
and radius `sqrt(g^2 + f^2 -c)`
= `sqrt(1/4 + 9/4 + (15)/4)` = 5/2