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Ellipse - Defination

Example 9
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Last updated at May 29, 2023 by Teachoo

Example 9 Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the latus rectum of the ellipse x225 + y29 = 1 Given 𝑥225 + 𝑦29 = 1 Since 25 > 9 Hence the above equation is of the form 𝑥2𝑎2 + 𝑦2𝑏2 = 1 Comparing (1) and (2) We know that c = 𝑎2−𝑏2 c = 25 −9 c = 16 c = 4 Coordinates of foci = ( ± c, 0) = (± 4, 0) So, coordinates of foci are (4, 0) & (−4, 0) Vertices = (± a, 0) = (± 5, 0) Thus vertices are (5, 0) and (–5, 0) Length of major axis = 2a = 2 × 5 = 10 Length of minor axis = 2b = 2 × 3 = 6 Eccentricity is e = 𝑐𝑎 = 45 Latus Rectum = 2𝑏2𝑎 = 2 × 95 = 185