Checkpoint: Graphing and Translating Ellipses Solution

Write the equation of an ellipse with a horizontal major axis of 12 units, a minor axis of 2 units, and a center at $(- 1, - 3)$ . Then graph.

$\begin{array}{rcl} \begin{matrix} a = \frac{12}{2} = 6 & b = \frac{2}{2} = 1 \\ a^{2} = 36 & b^{2} = 1 \end{matrix} \end{array}$

  $\frac{{(x + 1)}^{2}}{36} + \frac{{(y + 3)}^{2}}{1} = 1 \frac{{(x + 1)}^{2}}{36} + {(y + 3)}^{2} = 1$

Note

Q: Without graphing, how can you determine if the major axis is horizontal or vertical?

A: We know that if $a > b$ , it is horizontal, and if $b > a$ , it is vertical. 

Q: Describe the transformation to translate the ellipse to the origin.

A: The center of the ellipse would translate one unit right and three units up to be relocated at the origin.