First slide

Locus in 3D

Question

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

Moderate

A

$x^{2} + y^{2} - z^{2} = r^{2}$
B

$x^{2} + y^{2} + z^{2} = r^{2}$
C

$x^{2} + y^{2} - z^{2} = 2 r^{2}$
D

$x^{2} - y^{2} + z^{2} = r^{2}$

Solution

$W e h a v e x^{2} + y^{2} - z^{2} = r^{2} s e c^{2} α \cos^{2} β + r^{2} s e c^{2} α \sin^{2} β - r^{2} \tan^{2} α = r^{2}$

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