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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

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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 βˆ’ y2/16 = 1, The given equation is π‘₯2/9 βˆ’ 𝑦2/16 = 1 The above equation is of the form π‘₯2/π‘Ž2 βˆ’ 𝑦2/𝑏2 = 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 = (Β±c, 0) = (Β±5, 0) Thus, Co-ordinate of foci are (5, 0) & (βˆ’5, 0) Vertices = (Β±a, 0) = (Β±3, 0) Thus, Vertices are (3, 0) & (βˆ’3, 0) Eccentricity e = 𝑐/π‘Ž = πŸ“/πŸ‘ Latus rectum = 2𝑏2/π‘Ž = (2 Γ— 16)/3 = πŸ‘πŸ/πŸ‘

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.