The point $$\,\left( {4,\,1} \right)$$ undergoes the following three transformations successively.
Reflection about the line $$y=x$$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $$p/4$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.

A straight line $$L$$ is perpendicular to the line $$5x - y = 1.$$ The area of the triangle formed by the line $$L$$ and the coordinate axes is $$5$$. Find the equation of the Line $$L$$.

A square is inscribed in the circle $${x^2} + {y^2} - 2x + 4y + 3 = 0$$. Its sides are parallel to the coordinate axes. The one vertex of the square is

Two circles $${x^2} + {y^2} = 6$$ and $${x^2} + {y^2} - 6x + 8 = 0$$ are given. Then the equation of the circle through their points of intersection and the point (1, 1) is