Three lines $x + 2y + 3 = 0 ; x + 2y - 7 = 0$ and $2x - y - 4 = 0$ form the three sides of two squares. The equation to the fourth side of each square is
$2x - y + 14 = 0\,\,\, ane\,\, \,2x - y + 6 = 0$
$2x - y + 14 = 0\,\,\, ane\,\, \,2x - y - 6 = 0$
$2x - y - 14 = 0\,\,\, ane\,\, \,2x - y - 6 = 0$
$2x - y - 14 = 0\, ane \,2x - y + 6 = 0$
If the straight lines $x + 3y = 4,\,\,3x + y = 4$ and $x +y = 0$ form a triangle, then the triangle 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
Let the circumcentre of a triangle with vertices $A ( a , 3), B ( b , 5)$ and $C ( a , b ), ab >0$ be $P (1,1)$. If the line $AP$ intersects the line $BC$ at the point $Q \left( k _{1}, k _{2}\right)$, then $k _{1}+ k _{2}$ is equal to.
In a rectangle $A B C D$, the coordinates of $A$ and $B$ are $(1,2)$ and $(3,6)$ respectively and some diameter of the circumscribing circle of $A B C D$ has equation $2 x-y+4=0$. Then, the area of the rectangle is
Given three points $P, Q, R$ with $P(5, 3)$ and $R$ lies on the $x-$ axis. If equation of $RQ$ is $x -2y = 2$ and $PQ$ is parallel to the $x-$ axis, then the centroid of $\Delta PQR$ lies on the line