Example 11 - Find ellipse vertices (13, 0), foci (5, 0) - Ellipse - Defination

Example,  11 - Chapter 11 Class 11 Conic Sections - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

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

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.