Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Question 4: Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x 2 - 9y 2 = 576 Solution 4: The given equation is 16x 2 â€“ 9y 2 = 576. It can be written as 16x 2 â€“ 9y 2 = 576 2 2 x y 1 36 64 2 2 x y 1 …(1) 2 2 6 8 2 2 x y On comparing equation (1) with the standard equation of hyperbola i.e., 1, we obtain a = 6 and b = 8. We know that a 2 + b 2 = c 2 . 2 c 36 64 100 c = 10 Therefore, The coordinates of the foci are (±10, 0). The coordinates of the vertices are (±6, 0). c 10 5 Eccentricity, e = a 6 3 a b 2 2 Length of latus rectum 2 2b 264 64 a 6 3 Question 5: Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5y 2 - 9x 2 = 36 Solution 5: The given equation is 5y 2 â€“ 9x 2 = 36. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ 2 2 y x 1 36 4 5 2 2 y x 1 ... 1 2 6 2 5 On comparing equation (1) with the standard equation of hyperbola i.e., 6 a = and b = 2. 5 We know that a 2 + b 2 = c 2 . 2 36 56 c 4 5 5 56 2 14 c 5 5 2 14 Therefore, the coordinates of the foci are 0, 5 . 6 The coordinates of the vertices are 0, 5 . 2 14 c 5 14 Eccentricity, e = a 6 3 5 Length of latus rectum = 2 2b 24 4 5 a 6 3 5 y a x b 2 2 1 2 2 , we obtain Question 6: Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y 2 - 16x 2 = 784 Solution 6: The given equation is 49y 2 â€“ 16x 2 = 784. It can be written as 49y 2 â€“ 16x 2 = 784 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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