If two diagonals of a parallelogram $ABCD$ are along the lines $x+3y=4$ and $6x-2y=7$, then parallelogram represents
(a) rectangle
(b) rhombus
(c) square
(d) cyclic quadrilateral
$\bf{Attempts}$ with the help of slope
Slope of $x+3y=4$ is $\displaystyle m_{1} = -\frac{1}{3}$ and slope of $6x-2y=7$ is $\displaystyle m_{2} = -\frac{6}{-2} = 3$
So we have $m_{1}\cdot m_{2} = -1$ . So parallelogram represent Rhombus and Square.
But answer given is only Rhombus, could someone explain me the reason, Thanks
The two diagonals of the parallelogram being perpendicular to each other only defines a rhombus, not a square in particular. A square is a special case of a rhombus, with equal angles.