If the center of the parallelogram formed by the lines `x+2y-2-0, x+2y+6=0, 3x+y-1=0, 3x+y+5=0` is `(alpha,beta)` then `alpha + beta` is equal to

The area of the parallelogram formed by lines 2x-y+3=0, 3x+4y-6=0,2x-y+9=0, 3x+4y+4=0 is (in sq units)

The area of the parallelogram formed by the lines 2x-3y+a=0, 3x-2y-a=0, 2x-3y+3a=0 and 3x-2y-2a=0 in square units , is

If (alpha,alpha^2) lies inside the triangle formed by the lines 2x+3y-1=0,x+2y-3=0,5x-6y-1=0 , then

The point of intersection of the pair of lines x^(2)+xy+2y^(2)-3x+2y+4=0 is (alpha,beta) then 2 alpha+beta=

Let the equation of a line through (3, 6, -2) and parallel to the planes x-y+2z=5 and 3x+y+2z=6 is L=0 . If point (alpha,beta, 2) satisfy L=0 , then alpha+2beta is equal to

Let the equation of a line through (3, 6, -2) and parallel to the planes x-y+2z=5 and 3x+y+2z=6 is L=0 . If point (alpha,beta, 2) satisfy L=0 , then alpha+2beta is equal to

The perimeter of a parallelogram whose sides are represented by the lines x+2y+3=0 , 3x+4y-5=0,2x+5=0 and 3x+4y-10=0 is equal to