Ex 11.4

Chapter 11 Class 11 Conic Sections
Serial order wise

Get live Maths 1-on-1 Classs - Class 6 to 12

Transcript

Ex 11.4, 2 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola ﷐y2﷮9﷯ - ﷐x2﷮27﷯ = 1 Given equation is ﷐𝑦2﷮9﷯ – ﷐𝑥2﷮27﷯ = 1 The above equation of hyperbola is of the form ﷐𝑦2﷮𝑎2﷯ – ﷐𝑥2﷮𝑏2﷯ = 1 ∴ Axis of Hyperbola is y-axis Comparing (1) & (2) a2 = 9 a = 3 & b2 = 27 b = ﷐﷮3 × 3 × 3﷯ b = 3﷐﷮𝟑﷯ Also, c2 = a2 +b2 Putting value of a2 & b2 c2 = 9 + 27 c2 = 36 c = 6 Co-ordinates of foci = (0, ±c) = (0, ±6) So, co-ordinate of foci are (0, 6) & (0, −6) Co-ordinates of Vertices = (0, ±a) = (0, ±3) So, co-ordinates of vertices are (0, 3) & (0, −3) Eccentricity = e = ﷐𝑐﷮𝑎﷯ = ﷐6﷮3﷯ = 2 Latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2 × 27﷮3﷯ = 18

Made by

Davneet Singh

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.