1. Class 11
2. Important Question for exams Class 11

Transcript

Example 10 Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x2 + 4y2 = 36. Given 9x2 + 4y2 = 36 Dividing whole equation by 36 ﷐9﷐𝑥﷮2﷯ + 4﷐𝑦﷮2﷯﷮36﷯ = ﷐36﷮36﷯ ﷐9﷮36﷯x2 + ﷐4﷐𝑦﷮2﷯﷮36﷯ = 1 ﷐﷐𝑥﷮2﷯﷮4﷯ + ﷐﷐𝑦﷮2﷯﷮9﷯ = 1 Since 4 < 9 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 = ﷐﷮9−4﷯ c = ﷐﷮𝟓﷯ Co-ordinate of foci = (0, ± c) = (0, ± ﷐﷮5﷯) So co-ordinates of foci (0, ﷐﷮5﷯), & (0, −﷐﷮5﷯) Vertices = (0, ± a) = (0, ± 3) So vertices are (0, 3) & (0, −3) Length of major axis = 2a = 2 × 3 = 6 Length of minor axis = 2b = 2 × 2 = 4 Eccentricity e = ﷐c﷮a﷯ = ﷐﷐﷮5﷯﷮3﷯ Length of latus rectum = ﷐2b2﷮a﷯ = ﷐2 × 4﷮3﷯ = ﷐8﷮3﷯

Class 11
Important Question for exams Class 11

About the Author

Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.