Complete the square to write the equation of the sphere in standard form. Find t

Reeves

Reeves

Answered question

2021-09-21

Complete the square to write the equation of the sphere in standard form. Find the center and radius.
x2+y2+z22x+6y+8z+1=0

Answer & Explanation

hosentak

hosentak

Skilled2021-09-22Added 100 answers

Using formula (x+a)2=x2+2xa+a2 write equation in more explicite way
x2+y2+z22x+6y+8z+1=0
(x22x+1)1+(y2+6y+9)9+(z2+8z+16)16+1=0
(x1)2+(Y+3)2+(z+4)2+11916=0
(x1)2+(y+3)2+(z+4)2=25
Now when equation looks like standart sphere equation we can tell that sphere has center at (1,-3,-4) and the radius is 5.
Result: (1,3,4), R=5

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