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Olin [163]
2 years ago
11

Find an equation of the sphere through the point (4,3,-1) and has center (3,8,1).

Mathematics
1 answer:
sleet_krkn [62]2 years ago
6 0

Answer:

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30

Step-by-step explanation:

The general equation of a sphere is as follows:

(x - x_{c})^{2} + (y - y_{c})^{2} + (z - z_{c})^{2} = r^{2}

In which the center is (x_{c}, y_{c}, z_{c}, and r is the radius.

In this problem, we have that:

x_{c} = 3, y_{c} = 8, z_{c} = 1

So

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = r^{2}

through the point (4,3,-1)

This leads us to find the radius.

(4 - 3)^{2} + (3 - 8)^{2} + (-1 - 1)^{2} = r^{2}

r^{2} = 1 + 25 + 4

r^{2} = 30

So the equation of the sphere is:

(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30

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