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Polar plane of a pole A of a sphere is locus of all points R where line through A meets points P and Q on sphere such that 2/AR = 1/AP + 1/AQ. How does polar plane of a pole of a sphere look like? Please provide a 3D view

abcdmath
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  • If $A$ is a point of a sphere and a line through $A$ meets the sphere at points $P$ and $Q$, then $P=A\lor Q=A$ (with a conjunction $P=Q=A$ in a case of the line tangent to the sphere). This implies either $AP=0$ or $AQ=0$ which makes the given condition meaningless – you can't divide $1$ by zero... – CiaPan Aug 20 '18 at 07:48

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HINT. Consider the particular case when $P$ is the point on the sphere nearest to $A$. By symmetry, the polar plane must be perpendicular to line $AP$.

For a 3D view, I'd suggest you to use GeoGebra.

Intelligenti pauca
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