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Example 12 - Find equation: foci (0, 5), major axis 20 - Examples

Example  12 - Chapter 11 Class 11 Conic Sections - Part 2
Example  12 - Chapter 11 Class 11 Conic Sections - Part 3

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Example 12 Find the equation of the ellipse, whose length of the major axis is 20 and foci are (0, ± 5). We need to find equation of ellipse Whose length of major axis = 20 & foci are (0, ± 5) Since the foci are of the type (0, ±c) So the major axis is along the y-axis & required equation of ellipse is 𝒙^𝟐/𝒃^𝟐 + 𝒚^𝟐/𝒂^𝟐 = 1 From (1) & (2) c = 5 Given length of major axis = 20 & We know that Length of major axis = 2a 20 = 2a 2a = 20 a = 20/2 a = 10 Also, c2 = a2 − b2 (5) 2 = (10) 2 − b2 (5) 2 = (10) 2 − b2 b2 = (10) 2 − (5) 2 b2 = 100 − 25 b2 = 75 Equation of ellipse is 𝑥^2/𝑏^2 + 𝑦^2/𝑎^2 = 1 Putting values 𝑥^2/75 + 𝑦^2/〖(10)〗^2 = 1 𝒙^𝟐/𝟕𝟓 + 𝒚^𝟐/𝟏𝟎𝟎 = 1

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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.