Ex 11.4, 7 - Chapter 11 Class 11 Conic Sections
Last updated at Feb. 6, 2020 by Teachoo
Last updated at Feb. 6, 2020 by Teachoo
Transcript
Ex 11.4, 7 Find the equation of the hyperbola satisfying the given conditions: Vertices (ยฑ2, 0), foci (ยฑ3, 0) Given Vertices are (ยฑ2, 0) Hence, vertices are on the x-axis โด Equation of hyperbola is of the form ๐๐/๐๐ โ ๐๐/๐๐ = 1 Now, Co-ordinate of vertices = (ยฑa, 0) & Vertices = (ยฑ2, 0) โด (ยฑa, 0) = (ยฑ2, 0) Hence a = 2 Also, Given coordinates of foci = (ยฑ3, 0) And we know that co-ordinates of foci are (ยฑc, 0) โด (ยฑc, 0) = (ยฑ3, 0) c = 3 Also c2 = a2 + b2 Putting a = 2, c = 3 32 = 22 + b2 9 = 4 + b2 5 = b2 b2 = 5 Also, Given coordinates of foci = (ยฑ3, 0) And we know that co-ordinates of foci are (ยฑc, 0) โด (ยฑc, 0) = (ยฑ3, 0) c = 3 Also c2 = a2 + b2 Putting a = 2, c = 3 32 = 22 + b2 9 = 4 + b2 5 = b2 b2 = 5 Thus, Equation of hyperbola ๐ฅ^2/๐^2 โ ๐ฆ^2/๐^2 = 1 ๐ฅ^2/2^2 โ ๐ฆ^2/5 = 1 ๐^๐/๐ โ ๐^๐/๐ = 1
Ex 11.4
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