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The latus rectum of a conic is the chord through the focus perpendicular to the axis. Find the positive difference between the latus-rectum lengths of the parabola 3y = x² + 4x - 9 and the ellipse x² + 4y² - 6x + 16y = 24.

1. 1/2
2. 2
3. 3/2
4. 5/2

Correct answer: 1/2

Solution

The parabola gives x² + 4x = 3y + 9, i.e. (x+2)² = 3(y +...) with 4p = 3 so latus rectum = 3. The ellipse becomes (x-3)²/49 + (y+2)²/(49/4) = 1 with latus rectum 2b²/a = 2*(49/4)/7 = 7/2. Difference = |3 - 7/2| = 1/2.

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