Example, 11 - Chapter 10 Class 11 Conic Sections

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Example, 11 Find the equation of the ellipse whose vertices are (± 13, 0) and foci are (± 5, 0) Given vertices are (± 13, 0) The given vertices are of the form (±a, 0) Hence the major axis is along x-axis & Equation of ellipse is of the form ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 From (1) & (2) a = 13 Also given coordinate of foci = (±5, 0) We know that foci = (± c, 0) So c = 5 We know that c2 = a2 − b2 (5) 2 = (13) 2 − b2 b2 = (13) 2 − (5) 2 b2 = 169 − 25 b2 = 144 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Putting value ﷐﷐𝒙﷮𝟐﷯﷮𝟏𝟔𝟗﷯ + ﷐﷐𝒚﷮𝟐﷯﷮𝟏𝟒𝟒﷯ = 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo