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Ex 11.4, 9 - Find hyperbola: Vertices (0, 3), foci (0, 5) - Hyperbola

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  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.4, 9 Find the equation of the hyperbola satisfying the given conditions: Vertices (0, ±3), foci (0, ±5) We need to find equation of hyperbola given Vertices (0, ±3), foci (0, ±5) Since Vertices are on the y-axis So required equation of hyperbola is ﷐𝑦2﷮𝑎2﷯ – ﷐𝑥2﷮𝑏2﷯ = 1 ∴ Axis of hyperbola is y−axis We know that Vertices = (0, ±a) & Given vertices = (0, ±3) ∴ (0, ±a) = (0, ±3) So a = 3 a2 = 9 Foci are (0, ± c) given vertices are (0, ±5) So c = 5 We know that c2 = a2 + b2 (5)2 = (3)2 + b2 25 = 9 + b2 −b2 = 9 − 25 −b2 = − 16 b2 = 16 Required equation of hyperbola is ﷐𝑦2﷮𝑎2﷯ − ﷐𝑥2﷮𝑏2﷯ = 1 Putting values ﷐𝒚𝟐﷮𝟗﷯ − ﷐𝒙𝟐﷮𝟏𝟔﷯ = 1

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