Example 14 (ii) - 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: (ii) y2 โ 16x2 = 16 The given equation is y2 โ 16x2 = 16 Divide whole equation by 16 (๐ฆ2โ16๐ฅ2)/16 = 16/16 ๐ฆ2/16 โ ๐ฅ2/1 = 1 The above equation is of the form ๐ฆ^2/๐^2 โ ๐ฅ^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 = โ๐๐ Co-ordinate of foci = (0, ยฑc) = (0, ยฑโ๐๐) So, co-ordinates of foci are (0, โ17) & (0, โโ17) Vertices = (0, ยฑa) = (0, ยฑ4) So, vertices are (0, 4) & (0, โ4) Eccentricity e = ๐/๐ = โ๐๐/๐ Latus rectum = 2๐2/๐ = (2 ร 1)/4 = ๐/๐
Examples
Example 2
Example 3 Important
Example 4 Important
Example 5
Example 6 Important
Example 7 Important
Example 8 Important
Example 9
Example 10 Important
Example, 11
Example 12 Important
Example 13 Important
Example 14 (i)
Example 14 (ii) Important You are here
Example 15
Example 16 Important
Example 17
Example 18 Important
Example, 19 Important
About the Author
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo