Question

Find the ratio in which the sphere x² + y² + z² = 504 divides the line joining the points (12, –4, 8) and (27, –9, 18).

Answer 1

Let the sphere meet the line joining the given points at the point (x₁, y₁, z₁).

Then, we have:

Suppose the point (x₁, y₁, z₁) divides the line joining the points (12, – 4, 8) and (27, – 9, 18) in the ratio λ:1.

∴

Substitute these values in equation (1):

Thus, the sphere divides the line joining the given points in the ratio 2:3 and 2:– 3.

Hence, the given sphere divides the line joining the points (12, – 4, 8) and (27, – 9, 18) internally in the ratio 2:3 and externally in the ratio −2:3.