A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, B respectively such that the area of the triangle with vertices (0, 0), A and B has a constant area C. The locus of the mid-point AB is given by the equation

A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching X-axis, the equation of the reflected ray is

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

Let each of the equations x² + 2xy + ay² = 0 and ax² + 2xy + y² = 0 represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by