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

Transcript

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 โˆ’ y2/16 = 1, The given equation is ๐‘ฅ2/9 โˆ’ ๐‘ฆ2/16 = 1 The above equation is of the form ๐‘ฅ2/๐‘Ž2 โˆ’ ๐‘ฆ2/๐‘2 = 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) & (โˆ’5, 0) Vertices = (ยฑa, 0) = (ยฑ3, 0) Thus, Vertices are (3, 0) & (โˆ’3, 0) Eccentricity e = ๐‘/๐‘Ž = ๐Ÿ“/๐Ÿ‘ Latus rectum = 2๐‘2/๐‘Ž = (2 ร— 16)/3 = ๐Ÿ‘๐Ÿ/๐Ÿ‘ Example 14 Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas: (ii) y2 โ€“ 16x2 = 16 The given equation is y2 โ€“ 16x2 = 16 Divide whole equation by 16 (๐‘ฆ2โˆ’16๐‘ฅ2)/16 = 16/16 ๐‘ฆ2/16 โˆ’ ๐‘ฅ2/1 = 1 The above equation is of the form ๐‘ฆ^2/๐‘Ž^2 โˆ’ ๐‘ฅ^2/๐‘^2 = 1 Comparing (1) & (2) a2 = 16 a = 4 & b2 = 1 b = 1 Also , c2 = a2 + b2 c2 = 16 + 1 c2 = 17 c = โˆš๐Ÿ๐Ÿ• Co-ordinate of foci = (0, ยฑc) = (0, ยฑโˆš๐Ÿ๐Ÿ•) So, co-ordinates of foci are (0, โˆš17) & (0, โˆ’โˆš17) Vertices = (0, ยฑa) = (0, ยฑ4) So, vertices are (0, 4) & (0, โˆ’4) Eccentricity e = ๐‘/๐‘Ž = โˆš๐Ÿ๐Ÿ•/๐Ÿ’ Latus rectum = 2๐‘2/๐‘Ž = (2 ร— 1)/4 = 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.