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Translation

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College Algebra

Definition

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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5 Must Know Facts For Your Next Test

  1. In analytic geometry, translating an ellipse involves adding or subtracting constants to its center coordinates.
  2. A translated ellipse maintains the same lengths for its major and minor axes.
  3. 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.
  4. Translating an ellipse does not affect its eccentricity.
  5. Graphing a translated ellipse requires adjusting the coordinates of all points according to the translation vector.

Review Questions

  • How do you modify the standard form equation of an ellipse to translate it?
  • What remains unchanged when you translate an ellipse?
  • If an ellipse centered at (0,0) is translated by (3,4), what will be its new center?

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