The lines $$2x + 3y + 19 = 0$$ and $$9x + 6y - 17 = 0$$ cut the coordinates axes in concyclic points.

The value of the expression $$\sqrt 3 \,\cos \,ec\,{20^0} - \sec \,{20^0}$$ is equal to

Lines$${L_1} = ax + by + c = 0$$ and $${L_2} = lx + my + n = 0$$ intersect at the point $$P$$ and make an angle $$\theta $$ with each other. Find the equation of a line $$L$$ different from $${L_2}$$ which passes through $$P$$ and makes the same angle $$\theta $$ with $${L_1}$$.

If the circle $${C_1}:{x^2} + {y^2} = 16$$ intersects another circle $${C_2}$$ of radius 5 in such a manner that common chord is of maximum lenght and has a slope equal to 3/4, then the coordinates of the centre of $${C_2}$$ are.............................