Chord AB is A Diameter Of The Sphere  with Coordinates Of A as (3, 2, –2). Find The Coordinates Of B.

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Question

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

Solution

Correct option is

 

The equation of the sphere is  .

 

 

 

 .

 Let B = (α, β, γ).   ∴ The mid-point of AB is (2, 1,– 6).

 

 

 

Testing

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

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

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.