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Ex 11.3, 4 - x2/25 + y2/100 = 1 Find foci, latus rectum - Ellipse - Defination

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.3, 4 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﷮25﷯ + ﷐y2﷮100﷯ = 1 ﷐﷐𝑥﷮2﷯﷮25﷯ + ﷐﷐𝑦﷮2﷯﷮100﷯ = 1 Since 25 < 100 Hence the above equation is of the form ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 Comparing (1) & (2) We know that c = ﷐﷮a2−b2﷯ c = ﷐﷮100−25﷯ c = ﷐﷮75﷯ c = 5﷐﷮𝟑﷯ Co-ordinate of foci = (0, ± c) = (0, ± 5﷐﷮3﷯) So co-ordinates of foci (0, 5﷐﷮3﷯), & (0, −5﷐﷮3﷯) Vertices = (0, ± a) = (0, ± 10) So vertices are (0, 10) & (0, −10) Length of major axis = 2a = 2 × 10 = 20 Length of minor axis = 2b = 2 × 5 = 10 Eccentricity e = ﷐c﷮a﷯ = ﷐5﷐﷮3﷯﷮10﷯ = ﷐﷐﷮3﷯﷮2﷯ Length of latus rectum = ﷐2b2﷮a﷯ = ﷐2 × 25﷮10﷯ = 5

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