Find the centre and radius of the following circles : `a(x^2 + y^2) - bx - cy = 0`

Explanation

`a(x^2 + y^2) - bx - cy = 0`
or, `x^2 + y^2 - (bx)a - (cy)/a = 0`
`therefore` 2g = -b/a, 2f = -c/a, c = 0
`therefore` g = -b/2a, f = -c/2a
`therefore` Centre at (-g, -f) = (b/2a, c/2a)
and radius = `sqrt(g^2 + f^2 - c) = sqrt((b^2)/(4a^2) + (c^2)/(4a^2))`
= `sqrt((b^2 + c^2)/(2a))`