Ex 11.3, 11 - Find equation Vertices (0, 13), foci (0, 5) - Ellipse - Defination

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
Ask Download

Transcript

Ex 11.3, 11 Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5) Given Vertices (0, ±13) Hence The vertices are of the form (0, ±a) Hence the major axis is along y-axis & equation of ellipse is of the form ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 From (1) & (2) a = 13 Also given coordinate of foci = (0, ±5) We know that foci are = (0, ±c) 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﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 Putting value ﷐﷐𝑥﷮2﷯﷮144﷯ + ﷐﷐𝑦﷮2﷯﷮169﷯ = 1

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail