Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Question 10: Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8. Solution 10: Foci (±5, 0), the transverse axis is of length 8. Here, the foci are on the x-axis. x Therefore, the equation of the hyperbola is of the form a Since the foci are (±5, 0), c = 5. Since the length of the transverse axis is 8, 2a = 8 ⇒ a = 4. We know that a 2 + b 2 = c 2 . ∴4 2 + b 2 = 52 ⇒ b 2 = 25 â€“ 16 = 9 Thus, the equation of the hyperbola is 2 2 x y 1 16 9 y . b 2 2 1 2 2 Question **11**: Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24. Solution **11**: Foci (0, ±13), the conjugate axis is of length 24. Here, the foci are on the y-axis. 2 2 y x Therefore, the equation of the hyperbola is of the form . a b Since the foci are (0, ±13), c = 13. Since the length of the conjugate axis is 24, 2b = 24 ⇒ b = 12. We know that a 2 + b 2 = c 2 . ∴a 2 + 12 2 = 13 2 ⇒ a 2 = 169 â€“ 144 = 25 Thus, the equation of the hyperbola is 2 2 y - 25 x = 1. 144 2 2 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 12: Find the equation of the hyperbola satisfying the give conditions: Foci 3 5,0 , the latus rectum is of length 8. Solution 12: Foci 3 5,0 , the latus rectum is of length 8. Here, the foci are on the x-axis. 2 2 x y Therefore, the equation of the hyperbola is of the form 1. 2 2 a b Since the foci are 3 5,0 , c = 3 5 Length of latus rectum = 8 2 2b = 8 a 2 b = 4a We know that a 2 + b 2 = c 2 . ∴a 2 + 4a = 45 ⇒ a 2 + 4a â€“ 45 = 0 ⇒ a 2 + 9a â€“ 5a â€“ 45 = 0 ⇒ (a + 9) (a â€“ 5) = 0 ⇒ a = â€“9, 5 Since a is non-negative, a = 5. ∴b 2 = 4a = 4 × 5 = 20 2 2 x y Thus, the equation of the hyperbola is 1. 25 20 Question 13: Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12. Solution 13: Foci (±4, 0), the latus rectum is of length 12. Here, the foci are on the x-axis. Therefore, the equation of the hyperbola is of the form Since the foci are (±4, 0), c = 4. Length of latus rectum = 12 2 2b 12 a 2 b = 6a We know that a 2 + b 2 = c 2 . x a y b 2 2 1 2 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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