The diagonals of a parallelogram PQRS are along the lines x+3y =4 and 6x-2y = 7, Then PQRS must be :

One diagonal of a square is along the line 8x-15 y=0 and one of its vertex is (1, 2). Then the equations of the sides of the square passing through this vertex are a. 23 x+7y=9,7x+23 y=53 b. 23 x-7y+9=0,7x+23 y+53=0 c. 23 x-7y-9=0,7x+23 y-53=0 d.none of these

The equation of the diagonal of the square formed by the pairs of lines xy +4x - 3y - 12 = 0 and xy - 3x +4 y - 12 = 0 is

Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. One diagonal of the parallelogram is 11x+7y=9. If the other diagonal is ax + by + c = 0, then

Points X and Y are taken on the sides QR and RS, respectively of a parallelogram PQRS, so that QX=4XR and RY=4YS The line XY cuts the line PR at Z Find the ratio PZ: ZR

If sum of the perpendicular distances of a variable point P(x, y) from the lines x + y - 5 = 0 " and " 3x - 2y + 6 = 0 is always 10. Show that P must move on a line.

Two sides of a rhombus ABCD are parallel to the lines y = x + 2 and y = 7x + 3 If the diagonals of the rhombus intersect at the point (1, 2) and the vertex A is on the y-axis, then vertex A can be

If the two consecutive sides of a parallelogram are 4x+5y=0 and 7x+2y=0 . If the equation of one diagonal is 11 x+7y=9, find the equation of the other diagonal.

Prove that the area of the parallelogram contained by the lines 4y-3x-a=0,3y-4x+a=0,4y-3x+3a=0, and 3y-4x+2a=0 is (2/7)a^2dot

If sum of the perpendicular distances of a variable point P(x, y) from the lines x+y-5= 0 and 3x - 2y +7=0 is always 10. Show that P must move on a line.

Two sides of a rhombus are along the lines, x-y+1=0 and 7x-y-5=0 . If its diagonals intersect at (-1,-2) , then which one of the following is a vertex of this rhombus ? (1) (-3,-9) (2) (-3,-8) (3) (1/3,-8/3) (4) (-(10)/3,-7/3)