Question

Show that the equation 3x² + 3y² + 6x – 4y – 1 = 0 represents a circle. Find its centre and radius.

Answer 1

Given equation is 3x² + 3y² + 6x – 4y – 1 = 0

Or x² + y² + 2x – 4/3 y – 1/3 = 0

The general equation of a circle is as follows:

x² + y² + 2gx + 2fy + c = 0

Where g, f and c are constants.

With

Centre: (-g, -f)

On comparing given equation with general form of circle, we have

2g = 2 ⇒ g = 1

2f = -4/3 ⇒ f = -2/3 and

c = -1/3

Now,

Centre (-g, -f) = (-1, 2/3)