Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Hyperbola
Ex 10.4, 4
Ex 10.4, 2
Ex 10.4, 3 Important
Ex 10.4, 6
Ex 10.4, 5 Important
Example 14 (i)
Ex 10.4, 7 Important
Example 15
Ex 10.4, 8
Ex 10.4, 9 Important You are here
Ex 10.4, 10
Ex 10.4, 11 Important
Ex 10.4, 12 Important
Ex 10.4, 13
Example 16 Important
Ex 10.4, 14 Important
Ex 10.4, 15 Important
Last updated at May 29, 2023 by Teachoo
Ex 10.4, 9 Find the equation of the hyperbola satisfying the given conditions: Vertices (0, ±3), foci (0, ±5) We need to find equation of hyperbola Given Vertices (0, ±3), foci (0, ±5) Since Vertices are on the y-axis So required equation of hyperbola is 𝒚𝟐/𝒂𝟐 – 𝒙𝟐/𝒃𝟐 = 1 ∴ Axis of hyperbola is y−axis We know that Vertices = (0, ±a) & Given vertices = (0, ±3) ∴ (0, ±a) = (0, ±3) So a = 3 Also, coordinates of foci are (0, ± c) Given, foci are (0, ±5) So, c = 5 We know that c2 = a2 + b2 (5)2 = (3)2 + b2 25 = 9 + b2 b2 = 25 − 9 b2 = 16 Required equation of hyperbola is 𝑦2/𝑎2 − 𝑥2/𝑏2 = 1 Putting values 𝑦2/32 − 𝑥2/16 = 1 𝒚𝟐/𝟗 − 𝒙𝟐/𝟏𝟔 = 1