If 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 is 10 square units , then a =

Ortho - centre of the triangle formed by the lines x - y = 0, x + y = 0, x = 3 is . . .

Find the area of the parallelogram formed by the lines 2x^2+5xy+3y^2=0 and 2x^2+5xy+3y^2+3x+4y+1=0

Orthocentre of the triangle formed by the lines xy-3x-5y+15=0 and 3x+5y=15 is

If the lines 2x+ y-3 = 0, 5x+ky - 3=0 and 3x -y -2 =0 are concurrent, find the value of k.

Show that the three straight lines 2x-3y + 5 = 0 , 3x + 4y - 7 = 0 and 9x- 5y + 8 = 0 meet in a point

Determine algebraically the vertices of the triangle formed by lines 3x - y = 3, 2x – 3y = 2 and x + 2y = 8 .

Find the area of the region bounded by the curves y =x^(2) +2, y =x, x =0 and x =3.

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them : (a) 7x + 5y + 6z + 30 = 0 and 3x - y-10z + 4 = 0 (b) 2x + y + 32 - 2 = 0 and x - 2y + 5 = 0 (c) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z-1 = 0 (d) 2x – y + 3z-1 = 0 and 2x - y + 3z + 3 = 0 (e) 4x + 8y + z - 8 = 0 and y + z - 4 = 0