Let $$\mathrm{ABC}$$ be a triangle with equations of its sides $$\mathrm{AB}, \mathrm{BC}$$. $$\mathrm{CA}$$ respectively are $$x-2=0, y-5=0$$ and $$5 x+2 y-10=0$$. Then the orthocentre of triangle lies on the line

For what value of $$\mathrm{a}$$ and $$\mathrm{b}$$ the intercepts cut off on the co-ordinate axes by the line $$a x-b y+8=0$$ are equal in length but opposite in signs to those cut off by the line $$2 x-3 y+6=0$$ on the axes

Find the direction in which a straight line must be drawn through the point $$(1,2)$$ so that its point of intersection with the line $$x+y=4$$ may be at a distance of $$\sqrt{\frac{2}{3}}$$ from this point.

The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$. The equation of the line is