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What is the length of the major axis of the ellipse x29+y22=1\frac{x^2}{9} + \frac{y^2}{2} = 1?\newlineWrite your answer in simplified, rationalized form.\newline__\_\_

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Find properties of ellipses from equations in general formright chevron icon

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Q. What is the length of the major axis of the ellipse x29+y22=1\frac{x^2}{9} + \frac{y^2}{2} = 1?\newlineWrite your answer in simplified, rationalized form.\newline__\_\_
  1. Identify lengths of axes: Given equation: (x2)/9+(y2)/2=1(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 (x2)/(a2)+(y2)/(b2)=1(x^2)/(a^2) + (y^2)/(b^2) = 1, where aa is the length of the semi-major axis and bb is the length of the semi-minor axis. The larger denominator corresponds to the semi-major axis. In the given equation, a2=9a^2 = 9 and b2=2b^2 = 2. Therefore, a=9a = \sqrt{9} and b=2b = \sqrt{2}.
  2. Calculate semi-major axis: Calculate the length of the semi-major axis.\newlineSince a=9a = \sqrt{9}, we find that a=3a = 3.\newlineThe length of the semi-major axis is 33 units.
  3. Determine length of major axis: Determine the length of the major axis.\newlineThe length of the major axis is twice the length of the semi-major axis.\newlineTherefore, the length of the major axis is 2×a=2×3=62 \times a = 2 \times 3 = 6 units.

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