Question

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

Answer 1

Answer:

$(x - 5)^{2} + (y - 6)^{2} + (z - 5)^{2} = 62$

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:

$x_{c} = 5, y_{c} = 6, z_{c} = 5$.

So

$(x - 5)^{2} + (y - 6)^{2} + (z - 5)^{2} = r^{2}$

through the point (6, 1, −1)

We use this to find the radius.

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

$r^{2} = 1 + 25 + 36 = 62$

So the equation of the sphere is:

$(x - 5)^{2} + (y - 6)^{2} + (z - 5)^{2} = 62$