10-6 Translating Conic Sections

Objectives To write the equation of a translated conic section

To identify a translated conic section from an equation

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In this lesson you will practice translation skills to locate ellipses and hyperbolas when their centers move from (0, 0) to (h, k). You will not need to relearn the geometry of these curves. Each will still depend on the same distances, a, b, and c that relate to their vertices and foci.

Essential Understanding In a relation with an x-y relationship, replacing x by x − h x minus h  and y by y − k y minus k  (with h > 0 h greater than 0  and k > 0 k greater than 0 ) translates the graph of the relation h units to the right and k units up.

The summary tables in this lesson are like those from the lesson on parabolas. Notice how each entry in the “Center (0, 0)” column relates to the corresponding entry in the “Center (h, k)” column.

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