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3D Coordinate Geometry

Equation of a sphere


If the two spheres (x4)2+(y1)2+z2=27(x-4)^2+(y-1)^2+z^2=27 and (x13)2+(y10)2+(z+9)2=a(x-13)^2+(y-10)^2+(z+9)^2=a are externally tangent to each other, what is the value of a?a?

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

The center of the sphere x210x+y2+z218z+99=0x^2-10x+y^2+z^2-18z+99=0 is (a,b,c).(a,b,c). Find the value of a+b+c.a+b+c.

The equation of a sphere centered at (4,6,5)(4,-6,-5) with radius 22 is x2+y2+z2+ax+by+cz+d=0.x^2+y^2+z^2+ax+by+cz+d=0. Find the value of a+b+c+d.a+b+c+d.

What is the radius of the sphere x2+y2+z2=22?x^2+y^2+z^2=22?


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