Ex 11.3, 12

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Ex 11.3, 12 Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0) Given Vertices (± 6, 0) The vertices are of the form (±a, 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) & (2) a = 6 Also given coordinate of foci = (±4, 0) We know that foci = (± c, 0) So c = 4 We know that c2 = a2 − b2 (4) 2 = (6) 2 − b2 b2 = (6) 2 − (4) 2 b2 = 36 − 16 b2 = 20 Equation of ellipse is ﷐﷐𝑥﷮2﷯﷮﷐𝑎﷮2﷯﷯ + ﷐﷐𝑦﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 Putting values ﷐﷐𝑥﷮2﷯﷮36﷯ + ﷐﷐𝑦﷮2﷯﷮20﷯ = 1