The correct option (A) (9/p2)
Explanation:
point on axis A(a, 0, 0), B(0, b, 0) and C(0, 0, c)
centroid of ΔABC(x1, y1, z1) = [(a/3), (b/3), (c/3)] A, B, C satisfied plane (x/a) + (y/b) + (z/c) = 1
also distance from (0, 0, 0) to plane is p
∴ p = [1/√{(1/a2) + (1/b2) + (1/c2)}]
∴ (1/p2) = (1/a2) + (1/b2) + (1/c2)
∴ (1/p2) = [1/(9x12)] + [1/(9y12)] + [1/(9z12)]
centroid of ΔABC is on (1/x2) + (1/y2) + (1/z2) = (9/p2).