The line joining two points $$A(2,0) B(3,1)$$ is rotated about $$A$$ in anticlockwise direction through an angle of $$15^{\circ}$$. If $$B$$ goes to $$C$$ in the new position, then the coordinates of $$C$$ is

The points on the $$x$$-axis whose perpendicular distance from the line $$\frac{x}{3}+\frac{y}{4}=1$$ is 4 units are

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