Question

Find centre and radius of the following circles

2x² + 2y² – 6x + 4y + 2 = 0

Answer 1

2x² + 2y² – 6x + 4y + 2 = 0

(÷ by 2) ⇒ x² + y² – 3x + 2y + 1 =0

Comparing this equation with the general form of the circle we get

2g = – 3

2f= 2

g = `- 3/2`

g = 1

c = 1

So centre = (– g, – f) = `(3/2, -1)`

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

= `sqrt(9/4 + 1 - 1)`

= `3/2`

∴ Centre = `(3/2, -1)` and radius = `3/2`