﻿ 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. : Kaysons Education

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.

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Question

Solution

Correct option is

Let  be the position vectors of the extremities (1, 0, 1) and (5, 4, 5) of the diameter.

Let  be the position vector of a general point (x, y, z) on the sphere.

The equation of the required sphere is

…(1)

…(2)

(2)

SIMILAR QUESTIONS

Q1

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.

Q2

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

Q3

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

Q4

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