Question

find the centre and radius of the sphere determined by the points (1,-5,-3),(0,-6,-1),(2,-2,3),(1,-2,0).​

Answer 1

Step-by-step explanation:

Let the sphere be x

2

+y

2

+z

2

+2ux+2vy+2wz+d=0

Given it passes through (1,0,0),(0,1,0),(0,0,1)

⇒1+2u+d=0,1+2v+d=0,1+2w+d=0

Now radius of the sphere is r=

u

2

+v

2

+w

2

−d

=

4

3

(d+1)

2

−d

, using above equations.

Now for minimum value of r,

dd

dr

2

=0⇒d=−

3

1

∴r

min

=

3

2