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Ex 11.3, 10 - Find ellipse: Vertices (5, 0) foci (4, 0) - Ellipse - Defination

Ex 11.3,  10 - Chapter 11 Class 11 Conic Sections - Part 2
Ex 11.3,  10 - Chapter 11 Class 11 Conic Sections - Part 3

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Transcript

Ex 11.3, 10 Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0) Given Vertices (±5, 0) Since the vertices are of form (± a, 0) Hence, Major axis is along x-axis and equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 From (1) & (2) a = 5 Also given coordinate of foci = (±4, 0) We know that foci = (± c, 0) So c = 4 We know that c2 = a2 − b2 (4) 2 = (5) 2 − b2 b2 = (5) 2 − (4) 2 b2 = 25 − 16 b2 = 9 b = ﷐﷮9﷯ b = 3 Hence b = 3 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Putting value ﷐﷐𝑥﷮2﷯﷮﷐(5)﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐(3)﷮2﷯﷯ = 1 ﷐﷐𝑥﷮2﷯﷮25﷯ + ﷐﷐𝑦﷮2﷯﷮9﷯ = 1 Which is required equation

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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.