The equation $${r^2}{\cos ^2}\left( {\theta - {\pi \over 3}} \right) = 2$$ represents

If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at

The straight lines $$x + 2y - 9 = 0,3x + 5y - 5 = 0$$ and $$ax + by - 1 = 0$$ are concurrent if the straight line $$35x - 22y + 1 = 0$$ passes through the point

The locus of points (x, y) in the plane satisfying $${\sin ^2}x + {\sin ^2}y = 1$$ consists of