Eccentricity is the ratio of which two distances measured from a point…

Question

Eccentricity is the ratio of which two distances measured from a point on the curve?

Accepted Answer

B. To the focus over to the directrix

1. Pick any point P on the curve, with F the focus and D the directrix.
2. Measure the distance from P to F and the distance from P to D.
3. Eccentricity is the first divided by the second, and it is the same for every P.
4. Using the vertex or the center in place of the directrix gives a ratio that changes from point to point.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.5 Conic Sections in Polar Coordinates_

Answer

To the vertex over to the focus

Answer

To the center over to the focus

Answer

To the directrix over to the pole

Eccentricity is the ratio of which two distances measured from a point on the curve?

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