Analytical Geometry in sphere

[Win_odd Dhamnekar]

Hello,

How to show that any four noncoplanar points( i-e points that do not lie in the same plane) determine sphere?

How to find the equation of sphere that passes through the points (0,0,0), (0,0,2), (1,-4,3) and , (0,-1,3)?

My attempt:-
I know the definition of sphere which is as follows:





Now, how can I use this knowledge to answer this question?

 

[Deleted member 4993]

Hello,

How to show that any four noncoplanar points( i-e points that do not lie in the same plane) determine sphere?

How to find the equation of sphere that passes through the points (0,0,0), (0,0,2), (1,-4,3) and , (0,-1,3)?

My attempt:-
I know the definition of sphere which is as follows:

View attachment 19268
View attachment 19269


Now, how can I use this knowledge to answer this question?

Using the points (0,0,0), (0,0,2), (1,-4,3) and , (0,-1,3) and equation (1.31), you can write 4 equations with 4 unknowns.

You can solve those 4 linear equations, using matrices.

 

[LCKurtz]

Here's a little something to use to check your work against: