Translate ellipse's equation and Graph

Ellipse not centered at origin

Below is the general from for the translation(h,k) of an ellipse with a vertical major axis.

Formula for Translation of ellipse

Compare the two ellipses below, the the ellipse on the left is centered at the origin, and the righthand ellipse has been translated to the right.

example of translation of ellipse

Practice Problems: Translating Ellipse

Horizontal Translations

Problem 1

Can you graph the translation of the ellipse represented by the following standard form equation

equation of ellipse translation
Problem 2

Can you graph the translation of the ellipse represented by the following standard form equation

equation of ellipse translation
Problem 3

Can you graph the translation of the ellipse represented by the following standard form equation

equation of ellipse translation

Vertical Translations

Problem 4

Below is the equation of an ellipse under a vertical translation. Can you graph this equation?

equation of ellipse translation
vertical translation of ellipse
Problem 5

Below is the equation of an ellipse under a vertical translation. Can you graph this equation?

equation of ellipse translation
vertical translation of ellipse by 2
Problem 6

Below is the equation of an ellipse under a vertical translation. Can you graph this equation?

equation of ellipse translation
vertical translation of ellipse by 3

Vertical and Horizontal Translations

Problem 7

Below is the equation of an ellipse under a vertical translation. Can you graph this equation?

equation of ellipse translation
vertical translation of ellipse by 3
Problem 8

Below is the equation of an ellipse under a vertical translation. Can you graph this equation?

equation of ellipse translation

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