Which of the two lines 2x + y - 3 = 0 and 4x + y + 5 = 0 is farther from the origin?

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

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 .

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 .

If the lines 3x - 4y- 7 = 0 and 2x - 3y- 5 = 0 are two diameters of a circle of area 49 pi square units, then the equation of the circle is :

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 equation of a straight line passing through the point of intersection of the lines : 3x +y-9 =0 and 4x + 3y-7=0 and perpendicular to the line 5x -4y + 1 =0.

Equation of the straight line which belongs to the system of straight lines a(2x+y-3)+b(3x+2y-5)=0 and is farthest from the pint (4,-3) is

Show that the lines 2x + 3y - 8 = 0 , x - 5y + 9 = 0 and 3x + 4y - 11 = 0 are concurrent.

Find the equation of the circle whose centre is the point of intersection of the lines 2x-3y+4=0and3x+4y-5=0 and passes through the origin.

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.