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 (xx0)2+(yy0)2+(zz0)2 = r2  (ax0)2+(0y0)2+(0z0)2 = r2 (0x0)2+(ay0)2+(0z0)2 = r2 (0x0)2+(0y0)2+(az0)2 = r2  (ax0)2+(0y0)2+(0ax0y0)2 = r2 (0x0)2+(ay0)2+(0ax0y0)2 = r2 (0x0)2+(0y0)2+(aax0y0)2 = r2  (ax0)2+y02+(a+x0+y0)2 = r2 x2+(ay0)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+(z3a)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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