Ellipse - Defination

Chapter 10 Class 11 Conic Sections
Concept wise

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Ex 10.3, 2 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﷮4﷯ + ﷐y2﷮25﷯ = 1 ﷐x2﷮4﷯ + ﷐y2﷮25﷯ = 1 Since 4 < 25 The above equation is of the form ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 Comparing (1) & (2) We know that c = ﷐﷮﷐𝑎﷮2﷯−﷐𝑏﷮2﷯﷯ c = ﷐﷮25−4﷯ c = ﷐﷮𝟐𝟏﷯ Coordinate of foci = (0, ± c) = (0, ± ﷐﷮21﷯) So co-ordinate of foci are (0, ﷐﷮21﷯) &(0, − ﷐﷮21﷯) Vertices = (0, ± a) = (0, ± 5) Thus, vertices are (0, 5) & (0, −5) Length of major axis = 2a = 2 × 5 = 10 Length of minor axis = 2b = 2 × 2 = 4 Eccentricity e = ﷐𝑐﷮𝑎﷯ = ﷐﷐﷮21﷯﷮5﷯ Latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2 × 4﷮5﷯ = ﷐8﷮5﷯

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.