﻿ Find the equation of the sphere which passes through the points (1,–3, 4), (1, –5, 2), (1, –3, 0) and has its centre on the plane x + y + z = 0. : Kaysons Education

# Find The Equation Of The Sphere Which Passes Through The Points (1,–3, 4), (1, –5, 2), (1, –3, 0) And Has Its Centre On The Plane x + Y + Z = 0.

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## Question

### Solution

Correct option is

Let the equation of the sphere be

…(1)

(1,–3, 4) is on the sphere.

…(2)

(1,–5, 2) is on the sphere.

…(3)

(1, –3, 0) is on the sphere.

…(4)

The centre (–u, –v, –w) of the sphere lies on the plane x + y + z = 0.

…(5)

(2) – (3)                                                  …(6)

(3) – (4)                                         …(7)

(6) + (7)

Putting the values of v and in (5), we get

Putting the values of u, v and w in (2), we get

This is the equation of the sphere.

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