Find The Equation Of The Sphere Passing Through The Points (0, 0, 0), (–1, 2, 0), (0, 1, –1) And (1, 2, 5).

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Question

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

None of these

diffcult

Solution

Correct option is

Let the equation of the sphere be

…(1)

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

(–1, 2, 0) is on the sphere.

() …(2)

(0, 1,–1) is on the sphere.

…(3)

(1, 2, 5) is on the sphere.

…(4)

…(5)

…(6)

.

This is the equation of the sphere.

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SIMILAR QUESTIONS

Q1

Find the value of for which the plane touches the sphere

easy View solution

Q2

Find the radius of the circular section of the sphere by the plane

diffcult View solution

Q3

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

diffcult View solution

Q4

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.

diffcult View solution

Q5

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

medium View solution

Q6

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.

diffcult View solution

Q7

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

easy View solution