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
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.
SIMILAR QUESTIONS
Find the value of for which the plane touches the sphere
Find the radius of the circular section of the sphere by the plane
Find the centre and radius of the circle in which the plane intersects the sphere
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.
Chord AB is a diameter of the sphere with coordinates of A as (3, 2, –2). Find the coordinates of B.
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.
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.