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Ex 11.4, 6 - 49y2 - 16x2 = 784 Find foci, latus rectum - Hyperbola

Ex 11.4,  6 - Chapter 11 Class 11 Conic Sections - Part 2
Ex 11.4,  6 - Chapter 11 Class 11 Conic Sections - Part 3

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Transcript

Ex 11.4, 6 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y2 16x2 = 784 49y2 16x2 = 784 Dividing whole equation by 784 49 784 y2 16 784 x2 = 784 784 2 16 2 49 = 1 2 42 2 72 = 1 So our equation is of the form 2 2 2 2 = 1 Axis of hyperbola is y-axis Comparing (1) and (2) a2 = 42 a = 4 b2 = 72 b = 7 Also, c2 = a2 + b2 c2 = 72 + 42 c2 = 49 + 16 c2 = 65 c = Coordinates of focus is (0, c) = (0, 65 ) So, foci are (0, 65 ) & (0, 65 ) Coordinates of vertices = (0, a) = (0, 4) So, co-ordinates of vertices are (0, 4) & (0, 4) Eccentricity is e = = 65 4 Latus rectum = 2 2 = 2 7 2 4 = 2 49 4 = 49 2

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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.