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.

Find the foot of the perpendicular from the point (-1, 2) on the st. line x- y +5 =0.

Find the bisector of acute angle between the lines x+y - 3 = 0 and 7x - y + 5 = 0

Find the greatest distance of the point P(10 ,7) from the circle x^2+y^2-4x-2y-20=0

Which of the st. lines 2x - y + 3 = 0 and x- 4y-7=0 is farther from the origin ?

Find the coordinates of the point at unit distance from the lines 3x-4y + 1 = 0, 8x +6y +1 = 0

Obtain the co-ordinates of the feet of perpendiculars drawn from the origin upon the lines 3x -5y + 2=0 and 4x- 3y + 5 = 0 and show that the equation of the st. line joining these feet is 26x + 53y = 11 .

The distance of the point (1, 2) from the line x+y+5 = 0 measured along with the line parallel to 3x-y=7 is equal to :

Find the distance of the point (2,3) from the line 2x-3y+9=0 measured along a line x-y+1=0.

Find the distance of the point (2,3) from the line 2x-3y+9=0 measured along the line 2x-2y+5=0

Find equation of the line which is equidistant from parallel lines 9x + 6y -7 = 0 and 3x + 2y+6 = 0 .