Q:- A variable plane passes through a fixed point (a,b,c) and meets the coordinate axes in A,B,C . Locus of the point common to the planes through A,B,C and parallel to coordinate plane is...............

A. a/x+b/y+c/z=1

B.x/a+y/b+z/c=1

C.ax+by+cz=1

D. None of these

Dear Tapasranjan

let equation of plane is

x/a1 + y/b1 + z/c1 =1

then co ordinate of A is (a1,0,0)  ,B is (0,b1,0) ,C is (0,0,c1)

this plane passes through (a,b,c)

so

 a/a1 +b/b1 + c/c1  =1 .....................(1)

equation of plane passes trough A and parallel to coordinate plane  is

 x= a1

equation of plane passes trough B and parallel to coordinate plane  is

 y= b1

equation of plane passes trough C and parallel to coordinate plane  is

 z= c1

let common poin in these plane is (x1,y1,z1)

 so x1=a1

     y1=b1

     z1=c1

put value of a1,b1,c1 in equation 1

a/x1 + b/y1 + c/z1 =1

so locus is

 a/x +b/y + c/z =1

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