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 · Accepted Answer

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.  (x−x0)2+(y−y0)2+(z−z0)2=r2  Replace x0 with -9, y0 with 3, z0 with 9 and r with 5.  (x−(−9))2+(y−3)2+(z−9)2−52  Simplify:  (x+9)2+(y−3)2+(z−9)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+(y−3)2+(10−9)2=25  Simplify:  (x+9)2+(y−3)2+1=25  Subtract 1 from each side:  (x+9)2+(y−3)2=24  CONCLUSION  Equation sphere: (x+9)2+(y−3)2+(10−9)2=25  Equation intersection with plane z=10: (x+9)2+(y−3)2=24

Jeffrey Jordon · Accepted Answer

If a sphere has center(a, b, c) and radius r, then its equation is  (x−a)2+(y−b)2+(z−c)2=r2  By this theorem, the equation of the sphere is:  (x+9)2+(y−3)3+(z−9)2=25  Substitue z = 10 into the equation above, you may then get the intersection equation.

alenahelenash · Accepted Answer

Result:(x+9)2+(y−3)2+1=25Solution:The equation of the sphere centered at (−9,3,9) with radius 5 is given by:(x+9)2+(y−3)2+(z−9)2=25The intersection of this sphere with the plane z=10 can be described by substituting z with 10 in the equation of the sphere:(x+9)2+(y−3)2+(10−9)2=25Simplifying further:(x+9)2+(y−3)2+1=25

star233 · Accepted Answer

To find the equation of the sphere centered at (−9,3,9) with radius 5, we can use the standard equation of a sphere in three-dimensional space:(x−h)2+(y−k)2+(z−l)2=r2 where (h,k,l) represents the center of the sphere and r is its radius. Substituting the given values, we have:(x+9)2+(y−3)2+(z−9)2=52Expanding this equation, we get:x2+18x+81+y2−6y+9+z2−18z+81=25Simplifying further, we have:x2+y2+z2+18x−6y−18z+171=25x2+y2+z2+18x−6y−18z+146=0Thus, the equation of the sphere is:x2+y2+z2+18x−6y−18z+146=0Now, let&#039;s find the equation which describes the intersection of this sphere with the plane z=10. Substituting z=10 into the equation of the sphere, we have:x2+y2+102+18x−6y−18(10)+146=0Simplifying further, we get:x2+y2+18x−6y+148=0Therefore, the equation that describes the intersection of the sphere with the plane z=10 is:x2+y2+18x−6y+148=0

karton · Accepted Answer

Step 1: Given:(x−x0)2+(y−y0)2+(z−z0)2=r2In this case, the center of the sphere is (−9,3,9) and the radius is 5. Therefore, the equation of the sphere is:(x+9)2+(y−3)2+(z−9)2=52Step 2: Now, let&#039;s find the intersection of this sphere with the plane z=10. To do this, we substitute z with 10 in the equation of the sphere:(x+9)2+(y−3)2+(10−9)2=52Simplifying this equation gives us:(x+9)2+(y−3)2+1=25Which can be further simplified as:(x+9)2+(y−3)2=24Thus, the equation that describes the intersection of the sphere with the plane z=10 is:(x+9)2+(y−3)2=24

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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