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.