Ex 11.3, 5 - Chapter 11 Class 11 Conic Sections

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Ex 11.3, 5 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﷮49﷯ + ﷐y2﷮36﷯ = 1 ﷐﷐𝑥﷮2﷯﷮49﷯ + ﷐﷐𝑦﷮2﷯﷮36﷯ = 1 Since 49 > 36 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 = ﷐﷮49−36﷯ c = ﷐﷮𝟏𝟑﷯ Coordinate of foci = (± c, 0) = (± ﷐﷮13﷯, 0) So coordinate of foci are (﷐﷮13﷯, 0), (−﷐﷮13﷯, 0) Vertices = (± a, 0) = (±7, 0) So vertices are (7, 0) & (−7, 0) Length of major axis = 2a = 2 × 7 = 14 Length of minor axis = 2b = 2 × 6 = 12 Eccentricity e = ﷐𝑐﷮𝑎﷯ = ﷐﷐﷮13﷯﷮7﷯ Latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2 × 36﷮7﷯ = ﷐72﷮7﷯