Translation is a type of transformation that shifts every point of a shape or graph a constant distance in a specified direction. In the context of ellipses, it involves moving the entire ellipse without changing its shape, size, or orientation.
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In analytic geometry, translating an ellipse involves adding or subtracting constants to its center coordinates.
A translated ellipse maintains the same lengths for its major and minor axes.
The general equation for a translated ellipse is $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the new center.
Translating an ellipse does not affect its eccentricity.
Graphing a translated ellipse requires adjusting the coordinates of all points according to the translation vector.