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Example 14 - Chapter 11 Class 11 Conic Sections - Part 5

Example 14 - Chapter 11 Class 11 Conic Sections - Part 6
Example 14 - Chapter 11 Class 11 Conic Sections - Part 7 Example 14 - Chapter 11 Class 11 Conic Sections - Part 8

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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 – 16x2 = 16 The given equation is y2 – 16x2 = 16 Divide whole equation by 16 (𝑦2βˆ’16π‘₯2)/16 = 16/16 𝑦2/16 βˆ’ π‘₯2/1 = 1 The above equation is of the form 𝑦^2/π‘Ž^2 βˆ’ π‘₯^2/𝑏^2 = 1 Comparing (1) & (2) a2 = 16 a = 4 & b2 = 1 b = 1 Also , c2 = a2 + b2 c2 = 16 + 1 c2 = 17 c = βˆšπŸπŸ• Co-ordinate of foci = (0, Β±c) = (0, Β±βˆšπŸπŸ•) So, co-ordinates of foci are (0, √17) & (0, βˆ’βˆš17) Vertices = (0, Β±a) = (0, Β±4) So, vertices are (0, 4) & (0, βˆ’4) Eccentricity e = 𝑐/π‘Ž = βˆšπŸπŸ•/πŸ’ Latus rectum = 2𝑏2/π‘Ž = (2 Γ— 1)/4 = 𝟏/𝟐

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