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.

If the line pass through the point(-3,-5) and intersect the ellipse x^2/4+y^2/9=1 at a point A and B . Then the locus of mid point of line joining A and B is

If a line passes through the point of intersection of the lines 2x+y=5,x-y=1 and having slope 2 then it also passes through the point

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 point (5, 1) and parallel to the line 7x – 2y + 5 = 0.

y = mx be a variable line (m is variable) intersect the lines 2x + y-2=0 and x-2y + 2 = 0 in P and Q.The locus of midpoint of segment of PQ is

A line L passing through the point (2,1) intersects the curve 4x^(2)+y^(2)-x+4y-2=0 at the point A and B .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 L.

The line passing through the point of intersection of x+y=2,x-y=0 and is parallel to x+2y=5, is