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equation of an ellipse

For an ellipse centered at $(h, k)$ there are two different standard equations:

Major axis parallel to the $x$ -axis: $\frac{{(x - h)}^{2}}{a^{2}} + \frac{{(y - k)}^{2}}{b^{2}} = 1$ , $(a > b > 0)$ .

Major axis parallel to the $y$ -axis: $\frac{{(x - h)}^{2}}{b^{2}} + \frac{{(y - k)}^{2}}{a^{2}} = 1$ , $(a > b > 0)$ .

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$