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  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise

Transcript

Ex 11.4, 13 Find the equation of the hyperbola satisfying the given conditions: Foci (ยฑ4, 0), the latus rectum is of length 12 Since the foci are on the x-axis. Hence, the required equation of the hyperbola is ๐’™๐Ÿ/๐’‚๐Ÿ โ€“ ๐’š๐Ÿ/๐’ƒ๐Ÿ = 1 Now, coordinates of foci are (ยฑc, 0) & given foci = (ยฑ4, 0) so, (ยฑc,0) = (ยฑ4,0) c = 4 Now, Latus rectum =2๐‘2/๐‘Ž Given latus rectum = 12 So, 2๐‘2/๐‘Ž=12 2b2 = 12a b2 = 6a We know that c2 = a2 + b2 Putting value of c & b2 (4)2 = a2 + 6a 16 = a2 + 6a a2 + 6a โˆ’ 16 = 0 a2 + 8a โˆ’ 2a โˆ’16 = 0 a(a + 8) โˆ’ 2 (a + 8) = 0 (a โˆ’ 2) (a + 8) = 0 So, a = 2 or a = -8 Since โ€˜aโ€™ is distance, it cannot be negative , So a = โˆ’8 is not possible โˆด a = 2, From (1) b2 = 6a b2 = 6 ร—2 b2 = 12 Thus, Required equation of hyperbola ๐‘ฅ2/๐‘Ž2 โˆ’ ๐‘ฆ2/๐‘2=1 Putting values ๐‘ฅ2/22 โˆ’ ๐‘ฆ2/12=1 ๐’™๐Ÿ/๐Ÿ’ โˆ’ ๐’š๐Ÿ/๐Ÿ๐Ÿ=๐Ÿ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.