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The figure below shows a system that separates two minerals from the ore containing them using an electric field.

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Find the length of the major or minor axes of an ellipse

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Q. The figure below shows a system that separates two minerals from the ore containing them using an electric field.

Identify Coefficients: Identify the coefficients for $x^2$ and $y^2$ to determine the lengths of the semi-major and semi-minor axes. $\newline$ $\frac{x^2}{9} + \frac{y^2}{2} = 1$ $\newline$ Here, $9$ is under $x^2$ and $2$ is under $y^2$ .
Compare Coefficients: Compare the coefficients to find which is larger, indicating the direction of the major axis. $\newline$ Since $9 > 2$ , the major axis is along the $x$ -axis.
Calculate Semi-Major Axis: The length of the semi-major axis $a$ is the square root of the larger coefficient. $a = \sqrt{9} = 3$
Calculate Major Axis: The length of the major axis is twice the length of the semi-major axis. $\newline$ Length of major axis = $2 \times a = 2 \times 3 = 6$

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