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 Values: First, let's identify the values of a^2 and b^2 from the equation of the ellipse. The equation is in the form (x^2)/a^2 + (y^2)/b^2 = 1, where a^2 is the larger denominator.Find a and b: In our equation, (x^2)/9 + (y^2)/2 = 1, we see that a^2 = 9 and b^2 = 2. Since 9 > 2, a^2 corresponds to the major axis.Calculate a: Now, we find the value of a by taking the square root of a^2. So, a = sqrt(9) = 3.Major Axis Length: The length of the major axis is 2 times the value of a, which means it's 2 * 3 = 6.

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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 Values: First, let's identify the values of $a^2$ and $b^2$ from the equation of the ellipse. The equation is in the form $(x^2)/a^2 + (y^2)/b^2 = 1$ , where $a^2$ is the larger denominator.
Find $a$ and $b$ : In our equation, $\frac{x^2}{9} + \frac{y^2}{2} = 1$ , we see that $a^2 = 9$ and $b^2 = 2$ . Since 9 > 2, $a^2$ corresponds to the major axis.
Calculate $a$ : Now, we find the value of $a$ by taking the square root of $a^2$ . So, $a = \sqrt{9} = 3$ .
Major Axis Length: The length of the major axis is $2$ times the value of $a$ , which means it's $2 \times 3 = 6$ .