The locus of the foot of the perpendicular from the origin on each member of the family `(4a+ 3)x - (a+ 1)y -(2a+1)=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

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

The foot of the perpendicular drawn from the origin to the plane x+y+z=3 is

The locus of the foot of the perpendicular, from the origin to chords of the circle x^(2)+y^(2)-4x-6y-3=0 which subtend a right angle at the origin,is:

The locus of the foot of the perpendicular drawn from the origin to any tangent to the hyperbola (x^(2))/(36)-(y^(2))/(16)=1 is

The coordinates of the foot of the perpendicular drawn from the origin to the plane 2x -3y +4z -6=0 are ……