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Last updated at Sept. 6, 2021 by Teachoo
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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: (i) x2/9 β y2/16 = 1, The given equation is π₯2/9 β π¦2/16 = 1 The above equation is of the form π₯2/π2 β π¦2/π2 = 1 Comparing (1) & (2) a2 = 9 a = 3 & b2 = 16 b = 4 Also, c2 = a2 + b2 c2 = 9 + 16 c2 = 25 c = 5 So, Co-ordinate of foci = (Β±c, 0) = (Β±5, 0) Thus, Co-ordinate of foci are (5, 0) & (β5, 0) Vertices = (Β±a, 0) = (Β±3, 0) Thus, Vertices are (3, 0) & (β3, 0) Eccentricity e = π/π = π/π Latus rectum = 2π2/π = (2 Γ 16)/3 = ππ/π