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Find the equation of the ellipse, centred at the origin with axes along the coordinate axes, that passes through (-3, 1) and has eccentricity sqrt(2/5).

1. 3x² + 5y² - 32 = 0
2. 5x² + 3y² - 32 = 0
3. 3x² + 5y² - 15 = 0
4. 5x² + 3y² - 48 = 0

Correct answer: 3x² + 5y² - 32 = 0

Solution

With b² = (3/5)a² and the point (-3,1): 9/a² + 1/((3/5)a²) = 1 gives a² = 32/3, leading to 3x² + 5y² = 32.

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