Question

Find centre and radius of the following circles

x² + y² + 6x – 4y + 4 = 0

Answer 1

x² + y² + 6x – 4y + 4 = 0

Comparing with the general form we get

2g = 6

2f = – 4

⇒ g = 3, /= – 2 and c = 4

Centre = (– g, – f)

= (– 3, 2)

Radius = `sqrt(g^2 + f^2 - "c")`

= `sqrt(9 + 4 - 4)`

= 3

∴ Centre = (– 3, 2) and radius = 3