The locus of the foot of the perpendicular from the origin to a straight line passing through (1,1) is

The locus of feet of perpendiculars drawn from origin to the straight lines passing through (2,1) is

The locus of the foot of the perpendicular drawn from origin to a variable line passing through fixed point (2,3) is a circle whose diameter is

The locus ofthe foot of the perpendicular from the centre of the hyperbola

The length of the perpendicular from the point (0,0) to the straight line passing through P(1,2) such that P- bisects the intercepted part between axes.

Find the locus of the foot of perpendicular from the point (2,1) on the variable line passing through the point (0,0).

Paragraph Consider a family of lines (4a+3)x-(a+1)y-(2a+1)=0 where a in R. The locus of the foot of the perpendicular from the origin on each member of this family,is

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . A straight line passes through the centre of locus of T . Then locus of the foot of perpendicular to it from origin is : (A) a straight line (B) a circle (C) a parabola (D) none of these

If the foot of the perpendicular from the origin to a straight line is at (3,-4), then find the equation of the line.