Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ 2 2 y x Or, 1 16 49 2 2 y x Or, 1 ... 2 2 1 4 7 On comparing equation (1) with the standard equation of hyperbola i.e., a = 4 and b = 7. We know that a 2 + b 2 = c 2 . 2 c 16 49 65 c 65 Therefore, The coordinates of the foci are0, 65 . The coordinates of the vertices are (0, ±4). c 65 Eccentricity, e = a 4 y a x b 2 2 1 2 2 , we obtain Length of latus rectum 2 2b 249 49 a 4 2 Question 7: Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0) Solution 7: Vertices (±2, 0), foci (±3, 0) Here, the vertices are on the x-axis. 2 x y Therefore, the equation of the hyperbola is of the form Since the vertices are (±2, 0), a = 2. Since the foci are (±3, 0), c = 3. We know that a 2 + b 2 = c 2 . 2 2 2 2 b 3 b 2 = 9 – 4 = 5 Thus, the equation of the hyperbola is 2 2 x y 1 4 5 2 2 a - 2 b = 1 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 ______________________________________________________________________________ Question 8: Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8) Solution 8: Vertices (0, ±5), foci (0, ±8) Here, the vertices are on the y-axis. Therefore, the equation of the hyperbola is of the form Since the vertices are (0, ±5), a = 5. Since the foci are (0, ±8), c = 8. We know that a 2 + b 2 = c 2 . 2 2 2 5 b 8 b 2 = 64 – 25 = 39 Thus, the equation of the hyperbola is 2 2 y - 25 x = 1. 39 y a x b 2 2 1 2 2 Question 9: Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5) Solution 9: Vertices (0, ±3), foci (0, ±5) Here, the vertices are on the y-axis. 2 2 y x Therefore, the equation of the hyperbola is of the form . Since the vertices are (0, ±3), a = 3. Since the foci are (0, ±5), c = 5. We know that a 2 + b 2 = c 2 . ∴3 2 + b 2 = 52 ⇒ b 2 = 25 â€“ 9 = 16 Thus, the equation of the hyperbola is 2 2 y - 9 x = 1. 16 a b 2 2 1 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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