If $$A(4,7), B(-7,8)$$ and $$C(1,2)$$ are the vertices of $$\triangle A B C$$, then the equation of perpendicular bisector of the side $$A B$$ is

The ratio in which the straight line $$3 x+4 y=6$$ divides the join of the points $$(2,-1)$$ and $$(1,1)$$ is

Find the equation of a line passing through the point $$(4,3)$$, which cuts a triangle of minimum area from the first quadrant.

If the orthocenter of the triangle formed by the lines $$2 x+3 y-1=0, x+2 y+1=0$$ and $$a x+b y-1=0$$ lies at origin, then $$\frac{1}{a}+\frac{1}{b}$$ is equal to