Sphere from tree points

Equation of sphere with three-point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a

Correct answer:

e =  0

Step-by-step explanation:

C: x0​+y0​+z0​=a (x−x0​)2+(y−y0​)2+(z−z0​)2 = r2  (a−x0​)2+(0−y0​)2+(0−z0​)2 = r2 (0−x0​)2+(a−y0​)2+(0−z0​)2 = r2 (0−x0​)2+(0−y0​)2+(a−z0​)2 = r2  (a−x0​)2+(0−y0​)2+(0−a−x0​−y0​)2 = r2 (0−x0​)2+(a−y0​)2+(0−a−x0​−y0​)2 = r2 (0−x0​)2+(0−y0​)2+(a−a−x0​−y0​)2 = r2  (a−x0​)2+y02​+(a+x0​+y0​)2 = r2 x2+(a−y0​)2+(a+x0​+y0​)2 = r2 x02​+y02​+(x0​+y0​)2 = r2  r = 6​ a x0​ = −a y0​ = −a z0​ = 3a  (x+a)2 + (y+a)2+(z−3a)2 = 6 a2  e=0

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Showing 2 comments:
Math student
how can you write  r=a.(2/3)1/2
is this applicable for all plane equation?

Dr Math
We found some bugs in this problem, but I think now is OK solution:

(x+a)2 + (y+a)2+(z-3a)2 = 6 a2





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