Ex 11.4, 4 - 16x2 - 9y2 = 576 Find foci, latus rectum - Hyperbola

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  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.4, 4 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 – 9y2 = 576 The given equation is 16x2 – 9y2 = 576. Dividing whole equation by 576 ﷐16𝑥2﷮576﷯ − ﷐9𝑦2﷮576﷯ = ﷐576﷮576﷯ ﷐𝑥2﷮36﷯ − ﷐𝑦2﷮64﷯ = 1 The above equation hyperbola is of the form ﷐𝑥2﷮𝑎2﷯ − ﷐𝑦2﷮𝑏2﷯ = 1 ∴ Axis of hyperbola is x−axis Comparing (1) & (2) a2 = 36 a = 6 & b2 = 64 b = 8 Also, c2 = a2 + b2 c2 = 36 + 64 c2 = 100 c = 10 Co-ordinates of foci = (±c, 0) = (±10, 0) So co-ordinate of foci are (10, 0) & (−10, 0) Vertices = (±a, 0) = (±6, 0) So, co-ordinates vertices are (6, 0) & (−6, 0) Eccentricity e = ﷐𝑐﷮𝑎﷯ = ﷐10﷮6﷯ = ﷐5﷮3﷯ Latus rectum = ﷐2𝑏2﷮𝑎﷯ = ﷐2 × 64﷮6﷯ = ﷐64﷮3﷯

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