Ex 11.3, 16

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Ex 11.3, 16 Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6) We need to find equation of ellipse Whose length of minor axis = 16 & foci = (0, ±6) Since foci is of the type (0, ±c) 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 = 6 Given length of major axis = 16 & we know that Length of manor axis = 2b 16 = 2b 2b = 16 b = ﷐16﷮2﷯ b = 8 Also, We know that c2 = a2 − b2 (6) 2 = a 2 − (8)2 (6) 2 + (8)2 = a 2 36 + 64 = a 2 100 = a2 a2 = 100 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ = 1 Putting values ﷐﷐𝑥﷮2﷯﷮﷐(8)﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮100﷯ = 1 ﷐﷐𝒙﷮𝟐﷯﷮𝟔𝟒﷯ + ﷐﷐𝒚﷮𝟐﷯﷮𝟏𝟎𝟎﷯ = 1 Which is required equation