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Question

A circle with centre (2,3,0) and radius 1 is drawn in the plane z=0. Let the equation of the sphere which passes through this circle and the point (1,1,1) be x2+y2+z2kxmynz+p=0..Find k+m+np?

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Solution

Equation of circle is given by, (x2)2+(y3)21=0 and plane is z=0
Thus equation of required sphere is given by,
(x2)2+(y3)21+λz=0
Given this sphere passes through (1,1,1)
(12)2+(13)21+λ1=0λ=5
Hence, the equation of sphere is,
(x2)2+(y3)21λz=0
x2+y24x6y5z+12=0
k+m+np=3

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