text: 1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
  3. Ex 11.4
  
  Transcript
  
  Ex 11.4, 4 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 9y2 = 576 The given equation is 16x2 9y2 = 576. Dividing whole equation by 576 16 2 576 9 2 576 = 576 576 2 36 2 64 = 1 The above equation hyperbola is of the form 2 2 2 2 = 1 Axis of hyperbola is x axis Comparing (1) & (2) a2 = 36 a = 6 & b2 = 64 b = 8 Also, c2 = a2 + b2 c2 = 36 + 64 c2 = 100 c = 10 Co-ordinates of foci = ( c, 0) = ( 10, 0) So co-ordinate of foci are (10, 0) & ( 10, 0) Vertices = ( a, 0) = ( 6, 0) So, co-ordinates vertices are (6, 0) & ( 6, 0) Eccentricity e = = 10 6 = 5 3 Latus rectum = 2 2 = 2 64 6 = 64 3
  
  Ex 11.4
explanation: The document is a transcript from a mathematics textbook, specifically from Chapter 11 on Conic Sections. It contains a detailed solution to a problem involving a hyperbola, where the coordinates of the foci and vertices, the eccentricity, and the length of the latus rectum are calculated. The document includes the question and the complete answer.
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distilabel_metadata.role: system
distilabel_metadata.content: 1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
  3. Ex 11.4
  
  Transcript
  
  Ex 11.4, 4 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 9y2 = 576 The given equation is 16x2 9y2 = 576. Dividing whole equation by 576 16 2 576 9 2 576 = 576 576 2 36 2 64 = 1 The above equation hyperbola is of the form 2 2 2 2 = 1 Axis of hyperbola is x axis Comparing (1) & (2) a2 = 36 a = 6 & b2 = 64 b = 8 Also, c2 = a2 + b2 c2 = 36 + 64 c2 = 100 c = 10 Co-ordinates of foci = ( c, 0) = ( 10, 0) So co-ordinate of foci are (10, 0) & ( 10, 0) Vertices = ( a, 0) = ( 6, 0) So, co-ordinates vertices are (6, 0) & ( 6, 0) Eccentricity e = = 10 6 = 5 3 Latus rectum = 2 2 = 2 64 6 = 64 3
  
  Ex 11.4
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a transcript from a mathematics textbook, specifically from Chapter 11 on Conic Sections. It contains a detailed solution to a problem involving a hyperbola, where the coordinates of the foci and vertices, the eccentricity, and the length of the latus rectum are calculated. The document includes the question and the complete answer.
  
  Label: question-and-answer