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Last updated at Feb. 6, 2020 by Teachoo
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Ex 11.4, 14 Find the equation of the hyperbola satisfying the given conditions: Vertices (ยฑ7, 0), e = 4/3 Here, the vertices are on the x-axis. Therefore, the equation of the hyperbola is of the form ๐๐/๐๐ โ ๐๐/๐๐ = 1 Now, coor#dinates of vertices are (ยฑ a,0) & Given vertices = (ยฑ7, 0), So, (ยฑ a,0) = (ยฑ7, 0), a = 7 We know that Eccentricity = e = ๐/๐ Given that e = 4/3 4/3 = ๐/๐ 4a = 3c Putting a = 7 4 ร 7=3 ๐ 28 = 3 c 3c = 28 c = ๐๐/๐ Also, we know that c2 = a2 + b2 Putting values (28/3)^2 = 49 + b2 784/9 = 49 + b2 b2 = (784 โ441)/9 b2 = ๐๐๐/๐ Required equation of hyperbola ๐ฅ2/๐2โ ๐ฆ2/๐2 =1 Putting values ๐ฅ2/7^2 โ ๐ฆ2/(343/9) =1 ๐๐/๐๐ โ ๐๐๐/๐๐๐ = 1
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