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Ex 11.3, 3 - x2/16 + y2/9 = 1 Find vertices, length of minor axis - Ellipse - Defination

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.3, 3 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 ﷐x2﷮16﷯ + ﷐y2﷮9﷯ = 1 ﷐﷐𝑥﷮2﷯﷮16﷯ + ﷐﷐𝑦﷮2﷯﷮9﷯ = 1 Since 16 > 9 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 = ﷐﷮16−9﷯ c = ﷐﷮𝟕﷯ Coordinate of foci = (± c, 0) = (± ﷐﷮7﷯, 0) So coordinate of foci are (﷐﷮7﷯, 0), (−﷐﷮7﷯, 0) Vertices = (± a, 0) = (±4, 0) So vertices are (4, 0) & (−4, 0) Length of major axis = 2a = 2 × 4 = 8 Length of minor axis = 2b = 2 × 3 = 6 Eccentricity e = ﷐𝑐﷮𝑎﷯ = ﷐﷐﷮7﷯﷮4﷯ Latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2 × 9﷮4﷯ = ﷐9﷮2﷯

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