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Ex 11.4, 4 - 16x2 - 9y2 = 576 Find foci, latus rectum - Hyperbola

Ex 11.4,  4 - Chapter 11 Class 11 Conic Sections - Part 2
Ex 11.4,  4 - Chapter 11 Class 11 Conic Sections - Part 3

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Transcript

Ex 11.4, 4 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 9y2 = 576 The given equation is 16x2 9y2 = 576. Dividing whole equation by 576 16 2 576 9 2 576 = 576 576 2 36 2 64 = 1 The above equation hyperbola is of the form 2 2 2 2 = 1 Axis of hyperbola is x axis Comparing (1) & (2) a2 = 36 a = 6 & b2 = 64 b = 8 Also, c2 = a2 + b2 c2 = 36 + 64 c2 = 100 c = 10 Co-ordinates of foci = ( c, 0) = ( 10, 0) So co-ordinate of foci are (10, 0) & ( 10, 0) Vertices = ( a, 0) = ( 6, 0) So, co-ordinates vertices are (6, 0) & ( 6, 0) Eccentricity e = = 10 6 = 5 3 Latus rectum = 2 2 = 2 64 6 = 64 3

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.