Find the equation of the sphere centered at (-9, 3, 9) with radius 5. Give an equation which describes the intersection of this sphere with the plane z = 10.

Dillard 2021-03-02 Answered
Find the equation of the sphere centered at (-9, 3, 9) with radius 5. Give an equation which describes the intersection of this sphere with the plane z = 10.
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Nichole Watt
Answered 2021-03-03 Author has 100 answers
Given: A circle with Center C = (-9,3,9) Radius r=5
General eqation for a sphere with center C=(x0,y0,z0) and radius r.
(xx0)2+(yy0)2+(zz0)2=r2
Replace x0 with -9, y0 with 3, z0 with 9 and r with 5.
(x(9))2+(y3)2+(z9)252
Simplify:
(x+9)2+(y3)2+(z9)2=25
The intersection of the sphere with the plane z=10 can then be found by replacing z in the equation of the sphere by 10.
(x+9)2+(y3)2+(109)2=25
Simplify:
(x+9)2+(y3)2+1=25
Subtract 1 from each side:
(x+9)2+(y3)2=24
CONCLUSION
Equation sphere: (x+9)2+(y3)2+(109)2=25
Equation intersection with plane z=10: (x+9)2+(y3)2=24
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Jeffrey Jordon
Answered 2021-10-06 Author has 2064 answers

If a sphere has center(a, b, c) and radius r, then its equation is

(xa)2+(yb)2+(zc)2=r2

By this theorem, the equation of the sphere is:

(x+9)2+(y3)3+(z9)2=25

Substitue z = 10 into the equation above, you may then get the intersection equation.

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