De excentriciteit
van een ellips,
waarvan grote as
dubbel zo lang is
als de kleine as,
bedraagt 		A.  \(\boldsymbol{\frac 12 }\)
B.  \(\boldsymbol{\frac {2\,\sqrt 5} {5} }\)
C.  \(\boldsymbol{\frac {\sqrt 3} {2} }\)
D.  \(\boldsymbol{\frac 14 }\)
E.  \(\boldsymbol{\frac {\sqrt 5} {2} }\)
A    B    C    D    E

[ 6-1793 - op net sinds 2.4.12-(E)-30.10.2023 ]

Translation in   E N G L I S H

Calculate the
eccentricity
of an ellipse,
whose major
axis is twice
as long as
the minor axis 		A.   \(\boldsymbol{\frac 12 }\)
B.   \(\boldsymbol{\frac {2\,\sqrt 5} {5} }\)
C.   \(\boldsymbol{\frac {\sqrt 3} {2} }\)
D.   \(\boldsymbol{\frac 14 }\)
E.   \(\boldsymbol{\frac {\sqrt 5} {2} }\)

Oplossing - Solution

\(a=2b \quad \quad a^2 = b^2 + c^2\\ e = \frac ca=\frac{\sqrt{a^2-b^2}}{a}=\frac{\sqrt{4b^2-b^2}}{a}=\frac{\sqrt{3b^2}}{2b}=\frac{\sqrt{3}}{2}\)
gricha