Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

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nuggetrc nuggetrc

16-02-2022
Mathematics

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Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

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Аноним Аноним · Answer 1 · 2022-02-16T01:38:56+01:00

Given:Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).To find:The equation of hyperbola.Solution:We have, directrices at y = ±2 so this hyparabola is along the y-axis.The standard form of hyperbola is ...(i)where, (h,k) is center, foci are and directrix are .On comparing foci, we getOn comparing directrix we getNow,Putting , we get Therefore, the equation of hyperbola is .