Find an equation of the sphere with center (−2, 3, 7) and radius 7.What is the intersection of this sphere with the yz-plane?

Question

asked Jun 8, 2021 124k views

1 Answer

Ricky Nelson · Answer 1 · 2021-06-14T14:38:10+0000

Answer:

The equation of the sphere with center (-2, 3, 7) and radius 7 is
(x+2)^(2)+(y-3)^(2)+(z-7)^(2) = 49 .

The intersection of the sphere with the yz-plane is
(y-3)^(2)+(z-7)^(2) = 49 .

Explanation:

We know that any sphere can be represented by the following equation:

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

Where:

,
,
- Coordinates of the center of the sphere, dimensionless.

- Radius of the sphere, dimensionless.

If
(h,k, s) = (-2,3,7) and
r = 7 , we obtain this expression:

(x+2)^(2)+(y-3)^(2)+(z-7)^(2) = 49

The intersection of the sphere with the yz-plane observe the following conditions:

x = 0 ,
$y \in \mathbb {R}$ ,
$z\in \mathbb{R}$

Hence, the expression above can be reduced into this:

(y-3)^(2)+(z-7)^(2) = 49