What is the length of the minor axis of the ellipse given by the equation 16x^2 + 25y^2 = 400?
Show the answer and explanation
Correct answer
A. 8
Principle or equation
For an ellipse in standard form x^2/a^2 + y^2/b^2 = 1, the lengths of the major and minor axes are 2a and 2b, where a > b.
Why this answer is correct
Divide both sides by 400 to get x^2/25 + y^2/16 = 1. Thus a^2 = 25 (so a = 5) and b^2 = 16 (so b = 4). Since a > b, the major axis length is 2a = 10 and the minor axis length is 2b = 8.
Example
For 9x^2 + 4y^2 = 36, divide by 36: x^2/4 + y^2/9 = 1, so a=3, b=2, minor axis length 4.
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