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Rom4ik [11]
2 years ago
11

Find an equation of the sphere with center (4, −12, 8) and radius 10.

Mathematics
1 answer:
Lorico [155]2 years ago
5 0

Answer:

Step-by-step explanation:

To find an equation of the sphere with center (4, −12, 8) and radius 10

(x-4)^2+(y+12)^2+(z-8)^2 = 100

intersection with xy-plane

Put z=0

(x-4)^2+(y+12)^2+(0-8)^2 = 100

(x-4)^2+(y+12)^2 = 36

(A circle with centre at (4,-12) and radius 6)

intersection with xz-plane

Put y =0

(x-4)^2+(0+12)^2+(z-8)^2 = 100

(x-4)^2+(z-8)^2 = -44

Sum of squares cannot be positive, so DNE

intersection with yz-plane

Put x=0

(0-4)^2+(y+12)^2+(z-8)^2 = 100

(y+12)^2+(z-8)^2 = 84

A circle in YZ plane with centre at y =-12 and z =8 and radius square root of 84

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