In a plane there are two families of lines `y=x+r, y=-x+r`, where `r in {0, 1, 2, 3, 4 }`. The number of squares of diagonals of length 2 formed by the lines is:

Consider the fourteen lines in the plane given by y=x+r, y=-x+r, where rin{0,1,2,3,4,5,6} . The number of squares formed by these lines whose diagonals are of length 2, is

Find the equations of the diagonals of the square formed by the lines x=o,y=0,x=1 and y=1

Find the values of x and y , if (3y -2) + (5 -4x)i=0 , where , x y in R.

The diagonal of the rectangle formed by the lines x^(2)-7x+6=0 and y^(2)-14y+40=0 is

Consider a family of lines (4a+3)x-(a+1)y-(2a+1)=0 where a in R a member of this family with positive gradient making an angle of 45with the line 3x-4y=2, is

Let R={(x,y):x,yepsilonA,x+y=5} where A={1,2,3,4,5} then R is

The image line of 2x-y-1=0 w.r.t 3x-2y+4=0 is

Paragraph Consider a family of lines (4a+3)x-(a+1)y-(2a+1)=0 where a in R. The locus of the foot of the perpendicular from the origin on each member of this family,is

If the two lines x+(a-1)y=1 and 2x+a^(2)y=1 , (a in R-{0}) are perpendicular , then the distance of their point of intersection from the origin is