Show that the equation 3x2 + 3y2 + 6x - 4y – 1 = 0 represents a circle. Find its centre and radius.
The general equation of a conic is as follows
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 where a, b, c, f, g, h are constants
For a circle, a = b and h = 0.
The equation becomes:
x2 + y2 + 2gx + 2fy + c = 0…(i)
Given, 3x2 + 3y2 + 6x - 4y – 1 = 0
Comparing with (i) we see that the equation represents a circle with 2g = 2 
g = 1, 2f = 
and 
.
Centre ( - g, - f) = { - 1, - (
)}
= ( - 1, 
).
Radius = 
1