Question

What is the intersection of this sphere with the yz-plane? find an equation of the sphere with center (−3, 2, 9) and radius 6?

Answer 1

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

$(x-a)^{2} + (y-b)^{2} + (z-c)^{2} = r^{2}$, 

so the equation of the sphere with center (-3, 2, 9) and radius 6 is :

$(x-(-3))^{2} + (y-2)^{2} + (z-9)^{2} = 6^{2}$

$(x+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36$


The yz plane is the set of all points (0, y, z), that is x is always 0.

For x=0, the plane

$(x+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36$

becomes 

$(0+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36$

$(y-2)^{2} + (z-9)^{2}=36-9=25= 5^{2}$

$(y-2)^{2} + (z-9)^{2}=5^{2}$

This is the circle with center (y, z)=(2, 9) and radius 5.