If any point on an ellipse is (3\sin\alpha, 5\cos\alpha), then what is the eccentricity of the ellipse?

Explanation

Let x = 3\sin\alpha and y = 5\cos\alpha. Squaring and dividing gives \frac{x^2}{9} + \frac{y^2}{25} = \sin^2\alpha + \cos^2\alpha = 1. This is an ellipse with a^2=9 and b^2=25. Since b \gt a, the major axis is along the y-axis. Eccentricity e = \sqrt{1 - a^2/b^2} = \sqrt{1 - 9/25} = \sqrt{16/25} = 4/5.

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