Position-Ratio of Point/Examples/R Approaching Infinity

Example of Position-Ratio of Point

Let $P$ and $Q$ be points in space.

Let $R$ be a point on the straight line passing through $P$ and $Q$.

Let $k$ denote the position-ratio of $R$.

As $R$ approaches the point at infinity on the left, $k \to -1$ from above.

As $R$ approaches the point at infinity on the right, $k \to -1$ from below.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text I$. Coordinates: $11$. Position-ratio of a point