Ex 11.3, 13 - Find ellipse: Ends of major axis (3, 0) - Ellipse - Defination

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.3, 13 Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2) We need to find equation of ellipse Given that End of major axis = (± 3, 0) We know that Ends of major axis are the vertices of the ellipse. Vertices of the ellipse = (±3, 0) Vertices of the ellipse is of the form (± a, 0) So required equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 From (1) & (2) a = 3 Also . End of minor axis = (0, ± b) (0, ±2) = (0, ± b) So, b = 2 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Putting values ﷐﷐𝑥﷮2﷯﷮﷐3﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐2﷮2﷯﷯ = 1 ﷐﷐𝑥﷮2﷯﷮9﷯ + ﷐﷐𝑦﷮2﷯﷮4﷯ = 1

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