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Ex 11.4, 1 - x2/16 - y2/9 = 1 Find foci, vertices - Hyperbola

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  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.4, 1 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola ﷐x2﷮16﷯ - ﷐y2﷮9﷯ = 1 Given equation is ﷐𝑥2﷮16﷯ − ﷐𝑦2﷮9﷯ = 1 The above equation is of the form ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ − ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 So axis of hyperbola is x-axis , Comparing (1) & (2) a2 = 16 a = 4 & b2 = 9 b = 3 Now, c2 = a2 + b2 c2 = 16 + 9 c2 = 25 c = 5 Co-ordinate of foci = (±c, 0) = (±5, 0) Hence co-ordinates of foci are (5, 0) & (−5, 0) Co-ordinate of vertices = (±a, 0) = (± 4,0) So, co-ordinates of vertices are (4, 0) & (−4, 0) Eccentricity = e = ﷐𝑐﷮𝑎﷯ = ﷐5﷮4﷯ Latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2(9)﷮4﷯ = ﷐9﷮2﷯

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