What is the length of the major axis of the ellipse given by the equation 9x^2 + 4y^2 = 36?
Show the answer and explanation
Correct answer
A. 6
Principle or equation
The standard form of an ellipse centered at the origin is x^2/a^2 + y^2/b^2 = 1, where a and b are the semi-major and semi-minor axes (a > b if the major axis is along x). The length of the major axis is 2a.
Why this answer is correct
Divide both sides by 36: x^2/4 + y^2/9 = 1. Here a^2 = 9 and b^2 = 4, so a = 3, b = 2. Since a > b, the major axis length is 2a = 6.
Example
For 4x^2 + 9y^2 = 36, the standard form is x^2/9 + y^2/4 = 1, so major axis length is 6.
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