Ex 10.4
Last updated at April 19, 2024 by Teachoo
Ex 10.4, 13 Find the equation of the hyperbola satisfying the given conditions: Foci (Âą4, 0), the latus rectum is of length 12 Since the foci are on the x-axis. Hence, the required equation of the hyperbola is đđ/đđ â đđ/đđ = 1 Now, coordinates of foci are (Âąc, 0) & given foci = (Âą4, 0) so, (Âąc,0) = (Âą4,0) c = 4 Now, Latus rectum =2đ2/đ Given latus rectum = 12 So, 2đ2/đ=12 2b2 = 12a b2 = 6a We know that c2 = a2 + b2 Putting value of c & b2 (4)2 = a2 + 6a 16 = a2 + 6a a2 + 6a â 16 = 0 a2 + 8a â 2a â16 = 0 a(a + 8) â 2 (a + 8) = 0 (a â 2) (a + 8) = 0 So, a = 2 or a = -8 Since âaâ is distance, it cannot be negative , So a = â8 is not possible â´ a = 2, From (1) b2 = 6a b2 = 6 Ă2 b2 = 12 Thus, Required equation of hyperbola đĽ2/đ2 â đŚ2/đ2=1 Putting values đĽ2/22 â đŚ2/12=1 đđ/đ â đđ/đđ=đ