Ex 11.4, 2 - y2/9 - x2/27 = 1 Find foci, eccentricity - Ex 11.4

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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 10.4, 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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

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.