Q. 34.0( 5 Votes )

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

Answer :

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 =




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