A variable plane passes through the point (f, g, h ) and meets the axes at L, M and N. If the planes through L,M,N and parallel to the axes at P, then prove the locus of P is `(f)/(x)+(g)/(y)+(h)/(z)=1`.

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 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 line passes through a fixed point (x_(1),y_(1)) and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes)

A variables plane passes through the point (1,2,3) and meets the coordinate axis is P,Q,R . Then the locus of the point common to the planes P,Q,R parallel to coordinates planes

A point P moves on the plane (x)/(a)+(y)/(b)+(z)/(c)=1 . The plane, drawn through prependicular to OP meets the axes in L,M,N. the palnes through L,M,N, parallel to the coordinate plane meet in a point Q, then show that the locus of Q is given by the equation : x^(-2)+y^(-2)z^(-2)=(1)/(ax)+(1)/(by)+(1)/(cz) .

A variable plane passes through a fixed point (1,-2,3) and meets the coordinates axes at points A,B, C then the point of intersection of the planes thorugh A,B ,C parallel to the coordinates planes lies on