Ex 11.3, 15 - Class 11

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Ex 11.3, 15 Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0) Given foci = (± 5, 0) Since the foci is of the type (±c,0) So the major axis is along the x-axis & required equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 From (1) & (2) c = 5 Also given length of major axis = 26 & we know that Length of major axis = 2a 26 = 2a 2a = 26 a = ﷐26﷮2﷯ a = 13 Also , c2 = a2 − b2 (5) 2 = (13) 2 − b2 b2 = (13) 2 − (5) 2 b2 = 169 − 25 b2 = 144 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Putting values ﷐﷐𝑥﷮2﷯﷮﷐(13)﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮144﷯ = 1 ﷐﷐𝒙﷮𝟐﷯﷮𝟏𝟔𝟗﷯ + ﷐﷐𝒚﷮𝟐﷯﷮𝟏𝟒𝟒﷯ = 1 Which is required equation