A plane passes through a fixed point (a,b,c). The locus of the foot of the perpendicular to it from the origin is a sphere of radius

A plane passes through a fixed point (a ,b ,c)dot The locus of the foot of the perpendicular to it from the origin is a sphere of radius a. 1/2sqrt(a^2+b^2+c^2) b. sqrt(a^2+b^2+c^2) c. a^2+b^2+c^2 d. 1/2(a^2+b^2+c^2)

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.

A variable line passes through the fixed point (alpha,beta) . The locus of the foot of the perpendicular from the origin on the line is,

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is

The variable coefficients a, b in the equation of the straight line (x)/(a) + (y)/(b) = 1 are connected by the relation (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) where c is a fixed constant. Show that the locus of the foot of the perpendicular from the origin upon the line is a circle. Find the equation of the circle.

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 variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2,0), (0,2) and (1,1) on the line is zero. Find the coordinate of the point P.

Let (2,3,-1) be the coodinates of the foot of the prependicular drown from the origin toa plane .Find equation of that plane.

The coordinates of the foot of the perpendicular drawn from the point P(x,y,z) upon the zx- plane are-

A variable plane passes through a fixed point (a,b,c) and meets the axes at A ,B ,a n dCdot The locus of the point commom to the planes through A ,Ba n dC parallel to the coordinate planes is