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Ex 11.3
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Ex 11.3
Last updated at March 16, 2023 by Teachoo
Ex 11.3, 6 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 x2100 + y2400 = 1 𝑥2100 + 𝑦2400 = 1 Since 100 < 400 Hence the above equation is of the form 𝑥2𝑏2 + 𝑦2𝑎2 = 1 Comparing (1) & (2) We know that c = a2−b2 c = 400−100 c = 300 c = 10 × 10 × 3 c = 10𝟑 Co-ordinate of foci = (0, ± c) = (0, ± 103) So coordinates of foci (0, 103), & (0, −103) Vertices = (0, ± a) = (0, ± 20) So vertices are (0, 20) & (0, −20) Length of major axis = 2a = 2 × 20 = 40 Length of minor axis = 2b = 2 × 10 = 20 Eccentricity e = ca = 10320 = 32 Length of latus rectum = 2b2a = 2 × 10020 = 10