Last updated at Feb. 6, 2020 by Teachoo
Transcript
Ex 11.4, 13 Find the equation of the hyperbola satisfying the given conditions: Foci (ยฑ4, 0), the latus rectum is of length 12 Since the foci are on the x-axis. Hence, the required equation of the hyperbola is ๐๐/๐๐ โ ๐๐/๐๐ = 1 Now, coordinates of foci are (ยฑc, 0) & given foci = (ยฑ4, 0) so, (ยฑc,0) = (ยฑ4,0) c = 4 Now, Latus rectum =2๐2/๐ Given latus rectum = 12 So, 2๐2/๐=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 โ 16 = 0 a2 + 8a โ 2a โ16 = 0 a(a + 8) โ 2 (a + 8) = 0 (a โ 2) (a + 8) = 0 So, a = 2 or a = -8 Since โaโ is distance, it cannot be negative , So a = โ8 is not possible โด a = 2, From (1) b2 = 6a b2 = 6 ร2 b2 = 12 Thus, Required equation of hyperbola ๐ฅ2/๐2 โ ๐ฆ2/๐2=1 Putting values ๐ฅ2/22 โ ๐ฆ2/12=1 ๐๐/๐ โ ๐๐/๐๐=๐
Ex 11.4
About the Author