Geometry

# Equation of a sphere

If the two spheres $(x-4)^2+(y-1)^2+z^2=27$ and $(x-13)^2+(y-10)^2+(z+9)^2=a$ are externally tangent to each other, what is the value of $a?$

Consider a sphere that is tangent to the $xy$-, $yz$-, and $xz$-planes. If the sphere passes through $(6,3,-3),$ what is the product of all distinct possible values of the sphere's radius.

The center of the sphere $x^2-10x+y^2+z^2-18z+99=0$ is $(a,b,c).$ Find the value of $a+b+c.$

The equation of a sphere centered at $(4,-6,-5)$ with radius $2$ is $x^2+y^2+z^2+ax+by+cz+d=0.$ Find the value of $a+b+c+d.$

What is the radius of the sphere $x^2+y^2+z^2=22?$

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