Example 14 - Chapter 11 Class 11 Conic Sections

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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 - y2 16 = 1, The given equation is 2 9 2 16 = 1 The above equation is of the form 2 2 2 2 = 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 = ( c, 0) = ( 5, 0) Thus, Co-ordinate of foci are (5, 0) & ( 5, 0) Vertices = ( a, 0) = ( 3, 0) Thus, Vertices are (3, 0) & ( 3, 0) Eccentricity e = = 5 3 The latus rectum = 2 2 = 2 16 3 = 32 3 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 2 16 2 16 = 16 16 y2 16 x2 1 = 1 The above equation is of the form 2 2 2 2 = 1 Comparing (1) & (2) a2 = 16 a = 4 & b2 = 1 b = 1 Also , c2 = a2 + b2 c2 = 16 + 1 c2 = 17 c = Co-ordinate of foci = (0, c) = (0, 17 ) So, co-ordinates of foci are (0, 17 ) & (0, 17 ) Vertices = (0, a) = (0, 4) So, vertices are (0, 4) & (0, 4) Eccentricity e = = 17 4 Latus rectum = 2 2 = 2 1 4 = 1 2