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Tapasranjan Das Grade: 12
        

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

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

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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Badiuddin


7 years ago
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