Show that the equation x² + y² – 4x + 6y – 5 = 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, x² + y² – 4x + 6y – 5 = 0

Comparing with (i) we see that the equation represents a circle with 2g = - 4 g = - 2, 2f = 6f = 3 and c = - 5.

Centre ( - g, - f) = { - ( - 2), - 3}

= (2, - 3).

Radius =