Find the ratio in which the sphere x2 + y2 + z2 = 504 divides the line joining the points (12, -4, 8) and (27, -9, 18). PLZZZZZZ GIVE THE ANSWER BY TODAY ITSELF!!!!!!!!!!!!!!!!. I will give thumbs up to those who will give me the answer!!!!!!!!!!!!!!!!.

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

Then,

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

Then,

Putting 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.

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