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

The equation $$8 x^2-24 x y+18 y^2-6 x+9 y-5=0$$ represents a