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

Find the equations of the diagonals of the square formed by the lines x=o,y=0,x=1a n dy=1.

If R={(x,y):x inNN,y in NN and x+2y=8} , then the number of elements of R will be____

Find the angle between the tangents drawn to y^2=4x , where it is intersected by the line y=x-1.

Let L be the line belonging to the family of straight lines (a+2b) x+(a-3b)y+a-8b =0, a, b in R, which is the farthest from the point (2, 2). If L is concurrent with the lines x-2y+1=0 and 3x-4y+ lambda=0 , then the value of lambda is

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is

The image of P(a,b) on the line y=-x is Q and the image of Q on the line y=x is R find the mid-point of P and R

If line 3x-a y-1=0 is parallel to the line (a+2)x-y+3=0 then find the value of adot

If two sides of a square are the part of the straight lines 5x-2y=13and5x-2y+16=0 then find the area of the square.

Column I|Column II Two vertices of a triangle are (5,-1)a n d(-2,3) . If the orthocentre is the origin, then the coordinates of the third vertex are|p. (-4,-7) A point on the line x+y=4 which lies at a unit distance from the line 4x+3y=10 is|q. (-7,11) The orthocentre of the triangle formed by the lines x+y-1=0,x-y+3=0,2x+y=7 is|r. (2,-2) If 2a ,b ,c are in A P , then lines a x+b y=c are concurrent at|s. (-1,2)

Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x - y = 0 .