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The problem: A variable plane passes through a fixed point (a,b,c) and cuts the coordinate axes at P, Q, R (where none of P, Q, R is the origin). The co-ordinates (x,y,z) of the center of the sphere passing through P, Q, R and the origin satisfy the equation

(A) a/x + b/y + c/z = 2

(B) x/a + y/b + z/c = 3

(C) ax + by + cz = 1

(D) ax + by + cz = a2 + b2 + c2


I took the variable plane as x/p + y/q + z/r = 1 and the sphere to be

(X-x)2 + (Y-y)2 + (Z-z)2 = R2 and substituting the values of (p, 0, 0), (q, 0, 0), (r, 0, 0) & (0, 0, 0) in it, I eventually arrived at:

p2 + q2 + r2 = 2px + 2qy + 2rz, which is an equation of a plane in x, y, z. Hence, I was able to eliminate option A(certainly not a plane).

Any hint from here? Other approaches also welcome.

  • 0
    Bhaskar, you might want to post your own solution and accept it if you have found it yourself, so that this question is settled.2011-05-06
  • 0
    The values should be $(p, 0, 0), (0, q, 0), (0, 0, r)$ as a plane can only cut each axis once.2011-05-25

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