# Ex 11.4, 5

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 11.4, 5 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5y2 – 9x2 = 36 Given equation is 5y2 – 9x2 = 36. Dividing whole equation by 36 5𝑦236 − 9𝑥236 = 3636 𝑦2365 − 𝑥24 = 1 The above equation is of the form 𝑦2𝑎2 − 𝑥2𝑏2 = 1 ∴ Axis of hyperbola is y-axis Comparing (1) & (2) a2 = 365 a = 𝟔𝟓 & b2 = 4 b = 2 Also, c2 = a2 + b2 c2 = 365 + 4 c2 = 36 + 205 c2 = 565 c2 = 565 c = 𝟐𝟏𝟒𝟓 Co−ordinate of foci = (0, ± c) = 0, ± 2145 So, co-ordinates of foci are 0, 2145 & 0, −2145 Coordinates of vertices = (0, ±a) = (0, ±65) So, co-ordinates of vertices are 0, 65 & 0,−65 Eccentricity is e = 𝑐𝑎 e = 214565 e = 2145 × 56 = 143 Latus rectum = 2𝑏2𝑎 = 2 × 2265 = 2 × 4 × 56 = 453

Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.