Β
Last updated at Sept. 6, 2021 by
Β
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Example 14 Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas: (ii) y2 β 16x2 = 16 The given equation is y2 β 16x2 = 16 Divide whole equation by 16 (π¦2β16π₯2)/16 = 16/16 π¦2/16 β π₯2/1 = 1 The above equation is of the form π¦^2/π^2 β π₯^2/π^2 = 1 Comparing (1) & (2) a2 = 16 a = 4 & b2 = 1 b = 1 Also , c2 = a2 + b2 c2 = 16 + 1 c2 = 17 c = βππ Co-ordinate of foci = (0, Β±c) = (0, Β±βππ) So, co-ordinates of foci are (0, β17) & (0, ββ17) Vertices = (0, Β±a) = (0, Β±4) So, vertices are (0, 4) & (0, β4) Eccentricity e = π/π = βππ/π Latus rectum = 2π2/π = (2 Γ 1)/4 = π/π
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Example 14 (i)
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