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Ex 11.3, 9 - 4x2 + 9y2 = 36 Find length of major axis, minor - Ellipse - Defination

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.3, 9 Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 4x2 + 9y2 = 36 Given 4x2 + 9y2 = 36. Divide equation by 36 ﷐4﷐𝑥﷮2﷯﷮36﷯ + ﷐9﷐𝑦﷮2﷯﷮36﷯ = ﷐36﷮36﷯ ﷐﷐𝑥﷮2﷯﷮9﷯ + ﷐﷐𝑦﷮2﷯﷮4﷯ = 1 Since 9 > 4 Hence the above equation is of the form ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Comparing (1) & (2) We know that c = ﷐﷮a2−b2﷯ c = ﷐﷮9−4﷯ c = ﷐﷮𝟓﷯ Co-ordinates of foci = (±c, 0) = (± ﷐﷮5﷯, 0) So co-ordinate of foci are (﷐﷮5﷯, 0) & (−﷐﷮5﷯, 0) Vertices = (± a, 0) = (± 3, 0) So vertices are (3, 0) & (−3, 0) Length of major axis = 2a = 2 × 3 = 6 Length of minor axis = 2b = 2 × 2 = 4 Eccentricity e = ﷐𝑐﷮𝑎﷯ = ﷐﷐﷮5﷯﷮3﷯ Length of Latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2 × 4﷮3﷯ = ﷐8﷮3﷯

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