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Example 14 - Find foci, vertices, eccentricity, latus rectum

Example 14 - Chapter 11 Class 11 Conic Sections - Part 2
Example 14 - Chapter 11 Class 11 Conic Sections - Part 3 Example 14 - Chapter 11 Class 11 Conic Sections - Part 4

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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 βˆ’ y2/16 = 1, The given equation is π‘₯2/9 βˆ’ 𝑦2/16 = 1 The above equation is of the form π‘₯2/π‘Ž2 βˆ’ 𝑦2/𝑏2 = 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) & (βˆ’5, 0) Vertices = (Β±a, 0) = (Β±3, 0) Thus, Vertices are (3, 0) & (βˆ’3, 0) Eccentricity e = 𝑐/π‘Ž = πŸ“/πŸ‘ Latus rectum = 2𝑏2/π‘Ž = (2 Γ— 16)/3 = πŸ‘πŸ/πŸ‘

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