Ex 11.4, 12 - Find hyperbola: foci (35, 0), latus rectum 8 - Ex 11.4

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  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.4, 12 Find the equation of the hyperbola satisfying the given conditions: Foci ( 3 5 , 0) , the latus rectum is of length 8. Co-ordinates of Foci is ( 3 5 , 0) Since foci is on the x-axis Hence equation of hyperbola is of the form x2 a2 y2 b2 = 1 . Also, We know that co-ordinates of foci are ( c, 0) So, ( 3 5 , 0) = ( c, 0) 3 5 = c c = 3 Now, c2 = a2 + b2 Putting c = 3 5 a2 + b2 = (3 5 )2 a2 + b2 = 3 3 5 5 a2 + b2 = 9 5 a2 + b2 = 45 Also it is given that Latus Rectum = 8 2 2 = 8 2b2 = 8a b2 = 8 2 b2 = 4a Now, our equations are a2 + b2 = 45 (1) b2 = 4a (2) Putting the value of b2 in (1) a2 + 4a = 45 a2 + 4a 45 = 0 a2 + 9a 5a 45 = 0 a(a + 9) 5(a + 9) = 0 (a + 9) (a 5) = 0 So, a = 5 or a = 9 Since a is distance, it can t be negative So a = 5 From (2) b2 = 4a b2 = 4 5 b2 = 20 Equation of hyperbola is 2 2 2 2 = 1 2 5 2 2 20 = 1 = 1

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