Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.

The equation of the sphere with center (-3, 2 , 5) and radius 4 is

The intersection of the sphere with the yz- plane gave the equation which is a 2D- circle with center (0,2,5) and radius .

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

where, and are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center,  (-3, 2 , 5) and radius 4 becomes

Then,

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The plane is where , then we set

Them the equation becomes

This equation is the equation of a 2D- circle with center (0,2,5) and radius

This is the part of the sphere that intersects with the yz-plane.

283 square feet

step-by-step explanation:

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