1Cademy - Example: Graphing a Horizontal Ellipse with Center $$(h, k)$$

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How to Graph an Ellipse with Center $(0, 0)$

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Example: Graphing a Horizontal Ellipse with Center $(h, k)$

To graph the ellipse defined by the equation $\frac{(x-3)^2}{9} + \frac{(y-1)^2}{4} = 1$ , first confirm it is in the standard form with center $(h, k)$ , which is $(3, 1)$ . Next, compare the denominators to determine the orientation. Since $9 > 4$ and the larger number is under the $(x-3)^2$ term, the major axis is horizontal. The distance from the center to the vertices is found using $a^2 = 9$ , which gives $a = \pm 3$ . The distance from the center to the endpoints of the minor axis uses $b^2 = 4$ , yielding $b = \pm 2$ . To sketch the ellipse, plot the center at $(3, 1)$ , move $3$ units horizontally left and right to place the vertices, and move $2$ units vertically up and down to place the minor axis endpoints.

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Updated 2026-05-25

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OpenStax Intermediate Algebra

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