Question

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

Answer 1

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 $(x-5)^{2}+(y-6)^{2}+(z-5)^{2} = 93$.