Prove that st. line 5x -2y - 1 = 0 is mid-parailel to the st. lines : 5x - 2y -9 =0 and 5x - 2y + 7 = 0.

Find the acute angles between the st. lines : 2x-y+3=0 and x+y-2=0 .

Find the coordinates of the those point on the line 3x+ 2y = 5 which are equisdistant from the lines 4x+ 3y - 7 = 0 and 2y - 5 = 0

Find the equation of the st. line that has y -intercept 4 and is parallel to the st. line 2x -3y = 7 .

Find the equation of the line passing through the intersection of the lines x + 2y - 3 = 0 and 4x - y + 7 = 0 and which is parallel to 5x - 4y - 20 = 0 .

Find the acute angles between the st. lines : y-3x-5=0 and 3y -x +6= 0 .

Prove that the equations of the st. lines x+y-1=0 and x-y-1= 0 can be written as x + y = 0 and x-y = 0 by shifting the origin to a suitable point.

Find the distance between the st. line 4x + 3y- 5 = 0 and the point (- 2, - 1).

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.

Prove that the st. line ax + by + c = 0 divides the join of (x_1, y_1) and (x_2, y_2) in the ratio -(ax_1 + by_1 +c)/(ax_2+ by_2+c) .

Find the slope and y-intercept of the st. line 5x + 6y = 7.