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The extremities of a diameter of a sp...

The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.

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We are given the extremities of the diameter as (0, 2, 0) and (0, 0, 4). Therefore, the equation of the sphere is `(x-0)(x-0)+(y-2)(y-0)+ (z-0)(z-4)=0`
`or x^(2)+y^(2)+z^(2)-2y-4x=0`.
This sphere clearly passes through the origin.
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