Area Of The Parallelogram Formed By The Lines y = Mx, Y = Mx + 1, y = Nxand y = Nx + 1 Equals.

If a, b, c are all unequal and different from one and the points  are collinear then ab + bc + ca =

Consider three points

              ,

               and

              , then

The lines p(p² + 1)x – y + q = 0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for

The number of integral values of m, for which the x-coordinates of the point of intersection of the lines 2x + 4y = 9 and 

y = mx + 1 is also an integral is

Let PS be the median of the triangle with vertices P(2, 2), Q(6, –1) andR(7, 3). The equation of the line passing through

(1, –1) and parallel toPS is

Let PQR be a right angled isosceles triangle, right angled at P(2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

The point (2, 1) is shifted through a distance  units measured parallel to the line x + y = 1 in the direction of decreasing ordinates to reach Q.The image of Q w.r.t. given line is

Given the family of lines a(2x + y + 4) + b(x – 2y – 3) = 0. The number of lines belonging to the family at a distance  from any point (2, –3) is

Given four lines with equations x + 2y – 3 = 0, 3x + 4y – 7 = 0,

2x + 3y – 4 = 0, 4x + 5y – 6 = 0, then

The area bounded by the curves