How do you find the equation of a

Kennedy Ford

Kennedy Ford

Answered question

2022-04-16

How do you find the equation of a plane that is tangent to both the sphere w/ radius 3 and center (1,1,1) and the sphere w/ radius 4 and center (2,3,4)?

Answer & Explanation

Gonarsu2dw8

Gonarsu2dw8

Beginner2022-04-17Added 19 answers

The equation of the first sphere is:
(x1)2+(y1)2+(z1)2=32
Expanding the squares:
x22x+1+y22y+1+z22x+1=9
Subtract 3 from both sides:
x22x+y22y+z22x=6...[1]
The equation of the second sphere is:
(x2)2+(y3)2+(z4)2=42
Expand the squares:
x24x+4+y26y+9+z28z+16=16
Subtract 29 from both sides:
x24x+y26y+z28z=13...[2]
Subtract equation [2] from equation [1]:
2x+4y+6z=19

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