Ex 10.4, 2 - Chapter 10 Class 11 Conic Sections
Last updated at April 19, 2024 by Teachoo
Ex 10.4
Last updated at April 19, 2024 by Teachoo
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 y29 - x227 = 1 Given equation is 𝑦29 – 𝑥227 = 1 The above equation of hyperbola is of the form 𝑦2𝑎2 – 𝑥2𝑏2 = 1 ∴ Axis of Hyperbola is y-axis Comparing (1) & (2) a2 = 9 a = 3 & b2 = 27 b = 3 × 3 × 3 b = 3𝟑 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 = 𝑐𝑎 = 63 = 2 Latus rectum = 2𝑏2𝑎 = 2 × 273 = 18