A variable plane at a constant distance p from the origin meets the coordinate axes in points A,B and C respectively.Through these points , planes are drawn parallel to the coordinate planes, show that locus of the point of intersection is `1/x^2+1/y^2+1/z^2=1/p^2`

A variable plane at constant distance p form the origin meets the coordinate axes at P,Q, and R. Find the locus of the point of intersection of planes drawn through P,Q, r and parallel to the coordinate planes.

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

A variable plane is at a distance p from the origin O and meets the set of rectangular axes OX_(i)(i=1,2,3) at points A_(i)(i=1,2,3) respectively. If planes are drawn through A_(1),A_(2),A_(3) which are parallel to the coordinate planes, then the locus of theri point of intersection is

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tetrahedron O A B C is x^(-2)+y^(-2)+z^(-2)=16p^(-2)

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A , B , C . Show that the locus of the centroid of the tehrahedron O A B Ci sx^(-2)+y^(-2)+z^(-2)=16p^(-2)dot

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

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is 1/x^2+1/y^2+1/z^2=1/p^2 .

Find the distances of the point P(2, 3, 2) from the coordinate planes.

A variable line through the point ((6)/(5),(6)/(5)) cuts the coordinate axes at the points A and B respectively. If the point P divides AB internally in the ratio 2:1 , then the equation of the locus of P is

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is x^(-2) + y^(-2) + z^(-2) = p^(-2) .