Let $PQR$ be a triangle in which $PQ=3$. From the vertex $R$,draw the altitude $RS$ to meet $PQ$ at $S$. Assume that $RS=\sqrt{3}$ and $PS=QR$. Then,$PR$ equals

Two adjacent sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. If the equation of one diagonal is $11x + 7y - 9 = 0$,find the equation of the other diagonal.

Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. If the equation to one diagonal is $11x + 7y = 9$,then the equation to the other diagonal is:

The points $(-a,-b), (a, b), (0,0)$ and $(a^{2}, ab)$ where $a \neq 0, b \neq 0$ are always

Let the equations of two adjacent sides of a parallelogram $ABCD$ be $2x - 3y = -23$ and $5x + 4y = 23$. If the equation of its one diagonal $AC$ is $3x + 7y = 23$ and the distance of $A$ from the other diagonal is $d$,then $50d^2$ is equal to $........$.

Three vertices of a triangle are $A(4, 3)$,$B(1, -1)$,and $C(7, k)$. The value$(s)$ of $k$ for which the centroid,orthocentre,incentre,and circumcentre of the $\Delta ABC$ lie on the same straight line is/are: