Ex 11.3, 17 - Find equation of ellipse: Foci (3, 0) a = 4 - Ellipse - Defination

  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex11.3, 17 Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4 Given Foci (±3, 0) The foci are of the form (±c, 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) on (2) c = 3 Also, given a = 4 We know that c2 = a2 − b2 (3) 2 = (4) 2 − b2 b2 = (4) 2 − (3) 2 b2 = 16 − 9 b2 = 7 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Putting values ﷐﷐𝑥﷮2﷯﷮﷐(4)﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮7﷯ = 1 ﷐﷐𝒙﷮𝟐﷯﷮𝟏𝟔﷯ + ﷐﷐𝒚﷮𝟐﷯﷮𝟕﷯ = 1 Which is required equation

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