If the co-ordinates of the middle point of the portion of a line intercepted between coordinate axes $(3,2)$, then the equation of the line will be

A vertex of square is $(3, 4)$ and diagonal $x + 2y = 1,$ then the second diagonal which passes through given vertex will be

The area of the parallelogram formed by the lines $y = mx,\,y = mx + 1,\,y = nx$ and $y = nx + 1$ equals

Locus of the image of point $ (2,3)$ in the line $\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,k \in R$ is  a:

Let the equation of two sides of a triangle be $3x\,-\,2y\,+\,6\,=\,0$ and $4x\,+\,5y\,-\,20\,=\,0.$ If the orthocentre of this triangle is at $(1, 1),$ then the equation of its third side is

If a variable line drawn through the point of intersection of straight lines $\frac{x}{\alpha } + \frac{y}{\beta } = 1$and $\frac{x}{\beta } + \frac{y}{\alpha } = 1$ meets the coordinate axes in $A$ and $B$, then the locus of the mid point of $AB$ is