Find the ratio in which the sphere x2 + y2 + z2 = 504 divides the line joining the point (12, -4, 8) and (27, -9, 18).
Given: A(12, -4, 8) and B(27, -9, 18)
To find: the ratio in which the line segment AB is divided by the sphere x2 + y2 + z2 = 504
Formula used:
Section Formula:
A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).
The coordinates of C is given by,
Let C(x, y, z) be any point on given plane and C divides AB in ratio k: 1
Therefore, m = k and n = 1
A(12, -4, 8) and B(27, -9, 18)
Coordinates of C using section formula:
On comparing:
Since, x2 + y2 + z2 = 504
Hence, the sphere divides AB in ratio 2 : 3
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