A variable line makes intercepts on the co-ordinate axes , the sum of whose squares is constant and equal to `k^2`. Show that the locus of the foot of the perpendicular from the origin to this line is `(x^2+ y^2)^2 (x^(-2)+ y^(-2))=k^2`.

The co-ordinates of the foot of the perpendicular from (0, 0) upon the line x+y=2 are

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

Find the locus of the foot of the perpendicular from the origin upon a stright line which always passes through the point (2,3).

A rod of length k slides in a vertical plane, its ends touching the coordinate axes. Prove that the locus of the foot of the perpendicular from the origin to the rod is (x^2+y^2)^3=k^2x^2y^2dot

Find the locus of the foot of the perpendicular from the point (a,0) to the straight line x-ty+at^(2)=0 , t being variable.

Find the foot of perpendicular drawn from the point (2, 2) to the line 3x - 4y + 5 = 0

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1.

The product of the perpendiculars from origin to the pair of lines a x^2+2h x y+b y^2 + 2gx + 2fy + c =0 is

The co-ordinates of the foot of perpendicular from (a, 0) on the line y=mx+(a)/(m) are

A circle of radius r passes through the origin and intersects the x-axis and y-axis at P and Q respectively. Show that the equation to the locus of the foot of the perpendicular drawn form the origin upon the line segment bar (PQ) is (x^(2)+y^(2))^(3)=4r^(2)x^(2)y^(2) .