What is the length of the major axis of the ellipse (x^2)/9 + (y^2)/2 = 1? Write your answer in simplified, rationalized form. ______

Identify lengths of axes: Given equation: (x^2)/9 + (y^2)/2 = 1. Identify the lengths of the semi-major and semi-minor axes. The standard form of an ellipse is (x^2)/(a^2) + (y^2)/(b^2) = 1, where a is the length of the semi-major axis and b is the length of the semi-minor axis. The larger denominator corresponds to the semi-major axis. In the given equation, a^2 = 9 and b^2 = 2. Therefore, a = √9 and b = √2.Calculate semi-major axis: Calculate the length of the semi-major axis. Since a = √9, we find that a = 3. The length of the semi-major axis is 3 units.Determine length of major axis: Determine the length of the major axis. The length of the major axis is twice the length of the semi-major axis. Therefore, the length of the major axis is 2 * a = 2 * 3 = 6 units.

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What is the length of the major axis of the ellipse $\frac{x^2}{9} + \frac{y^2}{2} = 1$ ? $\newline$ Write your answer in simplified, rationalized form. $\newline$ $\_\_$

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Algebra 2

Find properties of ellipses from equations in general form

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Q. What is the length of the major axis of the ellipse

\frac{x^2}{9} + \frac{y^2}{2} = 1

\newline

Write your answer in simplified, rationalized form.

\newline

\_\_

Identify lengths of axes: Given equation: $(x^2)/9 + (y^2)/2 = 1$ . Identify the lengths of the semi-major and semi-minor axes. The standard form of an ellipse is $(x^2)/(a^2) + (y^2)/(b^2) = 1$ , where $a$ is the length of the semi-major axis and $b$ is the length of the semi-minor axis. The larger denominator corresponds to the semi-major axis. In the given equation, $a^2 = 9$ and $b^2 = 2$ . Therefore, $a = \sqrt{9}$ and $b = \sqrt{2}$ .
Calculate semi-major axis: Calculate the length of the semi-major axis. $\newline$ Since $a = \sqrt{9}$ , we find that $a = 3$ . $\newline$ The length of the semi-major axis is $3$ units.
Determine length of major axis: Determine the length of the major axis. $\newline$ The length of the major axis is twice the length of the semi-major axis. $\newline$ Therefore, the length of the major axis is $2 \times a = 2 \times 3 = 6$ units.