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Consider the conic C: x²/16 + y²/12 = 1. Find the equation of a parabola having the same length of latus rectum as C.
- y² - 6x - 21 = 0
- y² - 6x + 3 = 0
- y² + 6x - 21 = 0
- y² + 6x + 3 = 0
Correct answer: y² - 6x - 21 = 0
Solution
Ellipse latus rectum = 2b²/a = 6, so the parabola has 4aₚ = 6; y² = 6(x +...) rearranges to y² - 6x - 21 = 0 for the matching-LR parabola.
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