Example 14 - Find foci, vertices, eccentricity, latus rectum

Example 14 - Chapter 11 Class 11 Conic Sections - Part 2
Example 14 - Chapter 11 Class 11 Conic Sections - Part 3
Example 14 - Chapter 11 Class 11 Conic Sections - Part 4

 

  1. Chapter 11 Class 11 Conic Sections (Term 2)
  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‘

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.