﻿ A plane passes through a fixed point (­a, b, c) and cuts axes in A, B, C. Find the locus of the centre of the sphere OABC.  : Kaysons Education

# A Plane Passes Through A Fixed Point (­a, B, C) And Cuts Axes In A, B, C. Find The Locus Of The Centre Of The Sphere OABC.

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## Question

### Solution

Correct option is

2

Let the equation of a plane passing through the fixed point (a, b, c) be

…(1)

…(2)

Putting                                          …(2)

Putting y = 0, z = 0in (1), we get px = 1   i.e., x = 1/p.

∴ A = (1/p, 0, 0). Similarly B = (0,1/q, 0), C=(0, 0, 1/r).

Let the equation of the sphere passing through O, A, B, C, be

…(3)

(0, 0, 0) is on the sphere (3).

A is on the sphere (3).

Similarly,

Let the centre of this sphere be ().

Putting the values of p, q, r in (2), we get

#### SIMILAR QUESTIONS

Q1

Find the centre and radius of the circle in which the plane  intersects the sphere

Q2

Find the equation of the sphere passing through the points (0, 0, 0), (–1, 2, 0), (0, 1, –1) and (1, 2, 5).

Q3

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.

Q4

Chord AB is a diameter of the sphere  with coordinates of A as (3, 2, –2). Find the coordinates of B.

Q5

Obtain the equation of the sphere described on the join of the points (2, –3, 4) and B(–5, 6, –7) as a diameter.

Q6

Obtain the equation of the sphere where the points (1, 0, 1) and (5, 4, 5) are the extremities of a diameter. Deduce the equation in Cartesian form. Also find the radius and the centre of the sphere.