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Given the equation of circle $x^{2} + y^{2} = a^{2}$ and the equation of the plane $z=0$

Why is the general equation of sphere through them written as $x^{2} + y^{2} + z^{2} - a^{2} + \lambda(z) = 0$

From where does the term $z^{2}$ comes in the picture ?

However in other cases, if equation of circle is $C$ and plane be $P$, we write sphere's equation as $ C + \lambda(P) = 0$

user1611542
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1 Answers1

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I don't know where hace you got last equation from, but the general fórmula of an sphere is $(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=a^2$. So if you don't hace the $z^2$ term, you wouldn't have an sphere, if $\lambda(P)$ is not equal to that value.

Josu Etxezarreta Martinez
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