A circle passes through the points of intersection of the lines `lamda x-y+1=0` and `x-2y+3=0` with the coordinates axes. Show that `lamda=2`.

If a circle passes through the points of intersection of the axes with the lines ax-y+1=0 and x-2y+3=0 then a=

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the feet of the perpendicular from the origin on the variable line L has the equation

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the middle point of the segment AB has the eqution

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the centroid of the variable triangle OAB has the equation (where O is origin )

If the four points of intersection of the lines 2x+y-1=0, x+2y+2=0 with the coondinate axes lie on a circle then its centre is

The equation of the line passing through the point of intersection of the lines 2x+3y-4=0, 3x-y+5=0 and the origin is

If the 4 points made by intersection of lines 2x-y+1=0, x-2y+3=0 with the coordinate axes are concylic then centre of circle is

The equation of the line passing through the point of intersection of the lines 2x+y+1=0, x-y-7=0 and the point (3, -2) is

Show that the locus of the centres of the circles passing through the points of intersections of the circles x^2+y^2=1 and x^2+y^2-2x+y=0 is x+2y=0