What is the intersection of this sphere with the yz-plane

NetherCraft 0

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.

Answer

The equation of the sphere with center (a,b,c) and radius r is Givne that the center of the sphere is (-3,2,5)and radius 4 Therefore equati on of the sphere is of the form (x+3)+y-2)+(z-5)4 Hence the equation of the sphere y +6x-4y-10z+22 0 ence the eauation ot the sphere The intersection of this sphere withyz-plane ie. x-0,is a circle with equation, given by y2 +2-4y-10z +22-0

(x+3)^2+(y-2)^2+(z-5)^2=4^2=16 is the equation of the
sphere.
yz-plane means x = 0
=>9+(y-2)^2+(z-5)^2=16
=>(y-2)^2+(z-5)^2 = 7
Therefore the intersection of this sphere with the yz-plane is a
circle of radius sqrt(7) and centre at (0,2,5).

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