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Example 12 - Find equation: foci (0, 5), major axis 20 - Ellipse - Defination

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  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Example 12 Find the equation of the ellipse, whose length of the major axis is 20 and foci are (0, ± 5). We need to find equation of ellipse Whose length of major axis = 20 & foci are (0, ± 5) Since the foci are of the type (0, ±c) So the major axis is along the y-axis & required equation of ellipse is ﷐﷐𝒙﷮𝟐﷯﷮﷐𝒃﷮𝟐﷯﷯ + ﷐﷐𝒚﷮𝟐﷯﷮﷐𝒂﷮𝟐﷯﷯ = 1 From (1) & (2) c = 5 Given length of major axis = 20 & we know that Length of major axis = 2a 20 = 2a 2a = 20 a = ﷐20﷮2﷯ a = 10 Also We know that c2 = a2 − b2 (5) 2 = (10) 2 − b2 b2 = (10) 2 − (5) 2 b2 = 100 − 25 b2 = 75 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Putting value ﷐﷐𝑥﷮2﷯﷮75﷯ + ﷐﷐𝑦﷮2﷯﷮﷐(10)﷮2﷯﷯ = 1 ﷐﷐𝒙﷮𝟐﷯﷮𝟕𝟓﷯ + ﷐﷐𝒚﷮𝟐﷯﷮𝟏𝟎𝟎﷯ = 1

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