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$The locus of the point (r \sec α \cos β, r \sec α \sin β, r \tan α) is$

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x2+y2−z2=r2

x2+y2+z2=r2

x2+y2−z2=2r2

x2−y2+z2=r2

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detailed solution

Correct option is A

We have x2+y2-z2=r2sec2αcos2β+r2sec2αsin2β-r2tan2α =r2

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The locus of the point (rsec⁡αcos⁡β,rsec⁡αsin⁡β,rtan⁡α) is

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$The locus of the point (r \sec α \cos β, r \sec α \sin β, r \tan α) is$