Q. 94.8( 4 Votes )

# Find the ratio in which the sphere _{x}^{2} + y^{2} + z^{2} = 504 divides the line joining the point (12, -4, 8) and (27, -9, 18).

Answer :

**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 x^{2} + y^{2} + z^{2} = 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, x^{2} + y^{2} + z^{2} = 504

**Hence, the sphere divides AB in ratio 2 : 3**

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