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Test On Spheres

Probability Introduction :

Q1) What is the distance from the point (2, 8, 10) to the xz-plane?

Q2) Find an equation of the sphere with center (2, -3, 4) and radius 5 ?

Q3) Find the center and radius of the sphere  

     \(x^{2}+6x+y^{2}-4x+z^{2}-16z=-13 \)?

Q4) Find an equation of the largest sphere with center (5, 6 , 7) that is

       contained completely in the first octant ?

Q5) Find the equation of a sphere if one of its diameters has endpoints

      (-14, -12, -10) and (10, 12, 14) ?

Q6) Two spheres with the same radius r, one centered at (1,2,-4) and the other 

       centered at (2,4,3), touch each other tangentially at a single point. Find the

        value of the radius r.




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