Explanation:

Let the plane cuts the axes at A(l, 0, 0), B(0, m, 0), C(0, 0, n)

∴ Equation of plane is, x / l + y / m + z / n = 1

It passes through (a, b, c)

∴ a / l + b / m + c / n = 1

Equation of sphere OABC, where O(0, 0, 0) is origin,

x² + y² + z² – l x – m y – n z = 0

Its centre is at (x’, y’, z’) with, x’ = l/2, y’ = m/2, z = n/2

∴ l = 2x’ , m = 2y’ , n = 2z’

Therefore locus of centre is: a / x + b / y + c / z = 2