# 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 =   Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Lecture on radical axis of 2 circles48 mins  Lecture on Common tangents & angle of intersection of 2 circles56 mins  Lecture on Tangents to a Circle57 mins  General & parametric form of circle56 mins  Practice Problems on Equation of Circle54 mins  Family of circles55 mins  Quiz on Tangents to a Circle48 mins  Interactive Quiz on radical axis of 2 circles56 mins  Interactive Quiz on Locus involving circles42 mins  Interactive Quiz on Common tangents & angle of intersection of 2 circles56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 