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Ex 11.3, 14 - Find ellipse: ends of major axis (0, 5), minor - Ellipse - Defination

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.3, 14 Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (0, ± ﷐﷮5﷯) , ends of minor axis (±1, 0) Given end of major axis (0, ± ﷐﷮5﷯), & ends of minor axis (±1, 0) Major axis is along the y-axis So our required equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 We know that End of major axis is the vertices of the ellipse So vertices of ellipse = (0, ± ﷐﷮3﷯) Also, Vertices of the ellipse is (0, ± a) Comparing (0, ± a) = (0, ± ﷐﷮3﷯) a = ﷐﷮𝟑﷯ We know that End of minor axis = (± b, 0) So, (±1, 0) = (± b, 0) So, b = 1 Required equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 Putting values ﷐﷐𝑥﷮2﷯﷮﷐1﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐﷐﷐﷮5﷯﷯﷮2﷯﷯ = 1 ﷐﷐𝒙﷮𝟐﷯﷮𝟏﷯ + ﷐﷐𝒚﷮𝟐﷯﷮𝟓﷯ = 1

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