Find the equation of a sphere if one of it's diameter endpoints (-12,-1,-1) and (-2,-11,5)
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diameters has endpoints (0,7,4) and (1,9,7).(0,7,4) and (1,9,7).
Equations for Spheres:
In rectangular coordinates, a sphere has the general form of
(x−a)2+(y−b)2+(z−c)2=r2(x−a)2+(y−b)2+(z−c)2=r2,
where rr is the radius of the sphere with center (a,b,c)(a,b,c).
So to get the equation for the sphere, we need to find its radius and the center. We are given the endpoints, so the distance between them is the diameter, which is twice the radius. Also, the center is the midpoint between the endpoints.
Answer and Explanation:
Using the distance formula, we get the diameter of the sphere
{eq}\displaystyle d =2r = \sqrt{(1-0)^2 + (9-7)^2 + (7-4)^2} = \sqrt{1+4+9} =...
Equations for Spheres:
In rectangular coordinates, a sphere has the general form of
(x−a)2+(y−b)2+(z−c)2=r2(x−a)2+(y−b)2+(z−c)2=r2,
where rr is the radius of the sphere with center (a,b,c)(a,b,c).
So to get the equation for the sphere, we need to find its radius and the center. We are given the endpoints, so the distance between them is the diameter, which is twice the radius. Also, the center is the midpoint between the endpoints.
Answer and Explanation:
Using the distance formula, we get the diameter of the sphere
{eq}\displaystyle d =2r = \sqrt{(1-0)^2 + (9-7)^2 + (7-4)^2} = \sqrt{1+4+9} =...
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