Q9 of 84 Page 28

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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