Prove that the lines `2x+3y=19\ a n d\ 2x+3y+7=0` are equidistant from the line `2x+3y=6.`

Prove that the lines 2x+3y=19 and 2x+3y+7=0 are equidistant from the line 2x+3y=6 .

Prove that the lines x+3y+2=0 and 3x-y=0 are perpendicular.

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

Prove that the locus of a moving point, which is equidistant from the lines 3x-2y=5 and 3x+2y=5 , is a straight line.

Find the equation of the line passing through the intersection of the lines 2x+y=5\ a n d\ x+3y+8=0 and parallel to the line 3x+4y=7.

Find the equation of the line passing through the intersection of the lines 2x+y=5\ a n d\ x+3y+8=0 and parallel to the line 3x+4y=7.

Write the angle between the lines 2x=3y=z\ a n d\ 6x=-y=-4zdot

The equation of the line joining the point (3,5) to the point of intersection of the lines 4x+y-1=0 and 7x-3y-35=0 is equidistant from the points (0,0) and (8,34) .

Prove that the three lines 2x-y-5=0, 3x-y-6=0 and 4x-y-7=0 meet in a point.

Find the equation of the circle which touches the lines 4x-3y+10=0a n d4x-3y-30=0 and whose centre lies on the line 2x+y=0.