A variable line `L` passing through the point `B(2, 5)` intersects the lines `2x^2 - 5xy+2y^2 = 0` at P and Q. Find the locus of the point R on L such that distances BP, BR and BQ are in harmonic progression.

A variable line passing through point P(2,1) meets the axes at A and B . Find the locus of the circumcenter of triangle O A B (where O is the origin).

A line L passing through the point (2, 1) intersects the curve 4x^2+y^2-x+4y-2=0 at the point Aa n dB . If the lines joining the origin and the points A ,B are such that the coordinate axes are the bisectors between them, then find the equation of line Ldot

Find the equation of a line passing through the point of intersection of the lines 2x-7y+11=0 and x+3y=8 and passes through the point (2,-3) .

A variable line passing through the point P(0, 0, 2) always makes angle 60^(@) with z-axis, intersects the plane x+y+z=1 . Find the locus of point of intersection of the line and the plane.

The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

Find the equation of a line passing through the point (2,3) and parallel to the line 3x-4y+5=0 .

The line 5x + 4y = 0 passes through the point of intersection of straight lines x+2y-10 = 0, 2x + y =-5

Find the equation of a line passing through the point of intersection of the lines 3x+5y=-2 and 5x-2y=7 and perpendicular to the line 4x-5y+1=0 .

The point of intersection of the two lines given by 2x^2-5xy +2y^2-3x+3y+1=0 is

The line 5x + 4y = 0 passes through the point of intersection of straight lines (1) x+2y-10 = 0, 2x + y =-5