Example 14 (i) - Chapter 10 Class 11 Conic Sections
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 14 Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas: (i) x2/9 โ y2/16 = 1, The given equation is ๐ฅ2/9 โ ๐ฆ2/16 = 1 The above equation is of the form ๐ฅ2/๐2 โ ๐ฆ2/๐2 = 1 Comparing (1) & (2) a2 = 9 a = 3 & b2 = 16 b = 4 Also, c2 = a2 + b2 c2 = 9 + 16 c2 = 25 c = 5 So, Co-ordinate of foci = (ยฑc, 0) = (ยฑ5, 0) Thus, Co-ordinate of foci are (5, 0) & (โ5, 0) Vertices = (ยฑa, 0) = (ยฑ3, 0) Thus, Vertices are (3, 0) & (โ3, 0) Eccentricity e = ๐/๐ = ๐/๐ Latus rectum = 2๐2/๐ = (2 ร 16)/3 = ๐๐/๐
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