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marshall27 [118]
3 years ago
14

Find the equation of a sphere if one of its diameters has endpoints: (-9, -12, -6) and (11, 8, 14).

Mathematics
1 answer:
baherus [9]3 years ago
8 0

Answer:

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is (x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30.

Step-by-step explanation:

There are two kew parameters for a sphere: Center (h, k, s) and Radius (r). The radius is the midpoint of the line segment between endpoints. That is:

C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2}   \right)

C(x,y,z) = (1,-2,4)

The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:

r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}

r = 10\sqrt{3}

The general formula of a sphere centered at (h, k, s) and with a radius r is:

(x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is (x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30.

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