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Ex 10.4, 1
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola x2 16 - y2 9 = 1
Given equation is
2 16 2 9 = 1
The above equation is of the form
2 2 2 2 = 1
So axis of hyperbola is x-axis ,
Comparing (1) & (2)
a2 = 16
a = 4
&
b2 = 9
b = 3
Now,
c2 = a2 + b2
c2 = 16 + 9
c2 = 25
c = 5
Co-ordinate of foci = ( c, 0)
= ( 5, 0)
Hence co-ordinates of foci are (5, 0) & ( 5, 0)
Co-ordinate of vertices = ( a, 0)
= ( 4,0)
So, co-ordinates of vertices are (4, 0) & ( 4, 0)
Eccentricity = e = = 5 4
Latus rectum = 2 2 = 2(9) 4 = 9 2

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.

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