A variable plane passes through a fixed point `(a ,b ,c)` and cuts the coordinate axes at points `A ,B ,a n dCdot` Show that eh locus of the centre of the sphere `O A B Ci s a/x+b/y+c/z=2.`

Options

A. `x/a+y/b+z/c=1`
B. `a/x+b/y+c/z=1`
C. `a/x+b/y+c/z=2`
D. `x/a+y/b+z/c=2`

Answer

C

Explanation

Equation of plane passing through points (p,0,0),(0,q,0) and (0,0,r) and (0,0,r) is `x/p+y/q+z/r=1`
Given that this plane passes through (a,b,c).
`:. a/p+b/q+c/r=1`
Equation of spere is `x^2+y^2+z^2-px-qy-rz=0`
Centre of the sphere = (l, m, n)=`(p/2,q/2,r/2)`
`rArrp=2l,q=2m,r=2n`
`:."locus of the centre "rArr a/x+b/y+c/z=2`