Check sibling questions

Example 10 - 9x2 + 4y2 = 36, find foci, vertices, length

Example 10 - Chapter 11 Class 11 Conic Sections - Part 2
Example 10 - Chapter 11 Class 11 Conic Sections - Part 3
Example 10 - Chapter 11 Class 11 Conic Sections - Part 4

Solve all your doubts with Teachoo Black (new monthly pack available now!)


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 (9𝑥^2 + 4𝑦^2)/36 = 36/36 9/36 x2 + (4𝑦^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

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.