Locus of the points which are at equal distance from $3x + 4y - 11 = 0$ and $12x + 5y + 2 = 0$ and which is near the origin is
$21x - 77y + 153 = 0$
$99x + 77y - 133 = 0$
$7x - 11y = 19$
None of these
One side of a square is inclined at an acute angle $\alpha$ with the positive $x-$axis, and one of its extremities is at the origin. If the remaining three vertices of the square lie above the $x-$axis and the side of a square is $4$, then the equation of the diagonal of the square which is not passing through the origin is
The equation of the base of an equilateral triangle is $x + y = 2$ and the vertex is $(2, -1)$. The length of the side of the triangle is
The vertex of a right angle of a right angled triangle lies on the straight line $2x + y - 10 = 0$ and the two other vertices, at points $(2, -3)$ and $(4, 1)$ then the area of triangle in sq. units is
The number of possible straight lines , passing through $(2, 3)$ and forming a triangle with coordinate axes, whose area is $12 \,sq$. units , is