Ex 11.3, 7 - 36x2 + 4y2 = 144 Find foci, vertices, latus - Ex 11.3

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
Ask Download

Transcript

Ex 11.3, 7 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 36x2 + 4y2 = 144 Given 36x2 + 4y2 = 144. Dividing equation by 144 ﷐36﷐𝑥﷮2﷯﷮144﷯ + ﷐4﷐𝑦﷮2﷯﷮144﷯ = 1 ﷐1﷮4﷯x2 + ﷐1﷮36﷯y2 = 1 Since 4 < 36 Above equation is of form ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 Comparing (1) and (2) We know that c2 = a2 − b2 c2 = 32 c = ﷐﷮32﷯ c = 4﷐﷮𝟐﷯ Coordinate of foci = (0, ± c) = (0, ± 4﷐﷮2﷯) So coordinates of foci are (0, 4﷐﷮2﷯), (0, −4﷐﷮2﷯) Vertices = (0, ± a) = (0, ± 6) Thus, vertices are (0, 6) & (0, −6) Length of major axis = 2a = 2 × 6 = 12 Length of minor axis = 2b = 2 × 2 = 4 Eccentricity e = ﷐𝑐﷮𝑎﷯ = ﷐4﷐﷮2﷯﷮6﷯ = ﷐2﷐﷮2﷯﷮3﷯ Length of latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2 × 4﷮6﷯ = ﷐4﷮3﷯

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail