Translation

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.

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?

Related terms

Ellipse: A set of points such that the sum of the distances from any point on the shape to two fixed points (foci) is constant.

Transformation: An operation that moves or changes a shape in some way to produce a new shape.

Center: The midpoint between the foci of an ellipse; it is also equidistant from all vertices on an untransformed ellipse.