If the major axis of an ellipse is parallel to the \(X\)-axis and the ratio of the lengths of its latus rectum and minor axis is \(2:3\), then the ratio of distances from its centre to its focus and directrix is
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For an ellipse,
\[
\boxed{\text{Latus rectum}=\frac{2b^2}{a}}
\]
and
\[
\boxed{\text{Distance from centre to directrix}=\frac{a}{e}.}
\]
Also,
\[
\boxed{\frac{\text{Centre to focus}}{\text{Centre to directrix}}=e^2.}
\]