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Romashka [77]
3 years ago
12

Find an equation of the sphere that passes through the point (7, 1, −3) and has center (5, 6, 5).

Mathematics
1 answer:
xz_007 [3.2K]3 years ago
7 0

Answer:

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is (x-5)^{2}+(y-6)^{2}+(z-5)^{2} = 93.

Step-by-step explanation:

Any sphere centered at (h,k,s) in an Euclidean space with a radius r is represented by the following formula:

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

If (x,y,z) = (7,1,-3) and (h,k, s) = (5,6,5), the radius of the sphere is obtained:

(7-5)^{2}+(1-6)^{2}+(-3-5)^{2} = r^{2}

r^{2} = 93

r = \sqrt{93}

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is (x-5)^{2}+(y-6)^{2}+(z-5)^{2} = 93.

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