text: # show that the line X + Y equal to 8 intersect the parabola y square equal to 4 x at two points P and Q find the coordinates of the point equation of the chord PQ and its length is
  
  Aarya
  30 Points
  5 years ago
  X+Y=8
  X=8-Y--------------(1)
  Y^2=4X
  Y^2=4(8-Y)
  Y^2+4Y-32=0
  ON FINDING ROOTS, WE GET, Y=-8,+4
  SUBSTITUTING IN (1),
  IF Y=-8, X=16
  IF Y=+4, X=4
  HENCE, P=(16,-8)
  Q=(4,4)
  PQ=√[(16-4)^2+(-8-4)^2]
  PQ=√(144+144)
  PQ=12√2 SQ.UNITS
explanation: The document contains a math question and its corresponding answer. The question asks to show that the line \(X + Y = 8\) intersects the parabola \(y^2 = 4x\) at two points \(P\) and \(Q\), and to find the coordinates of these points, the equation of the chord \(PQ\), and its length. The answer provides a detailed step-by-step solution to the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # show that the line X + Y equal to 8 intersect the parabola y square equal to 4 x at two points P and Q find the coordinates of the point equation of the chord PQ and its length is
  
  Aarya
  30 Points
  5 years ago
  X+Y=8
  X=8-Y--------------(1)
  Y^2=4X
  Y^2=4(8-Y)
  Y^2+4Y-32=0
  ON FINDING ROOTS, WE GET, Y=-8,+4
  SUBSTITUTING IN (1),
  IF Y=-8, X=16
  IF Y=+4, X=4
  HENCE, P=(16,-8)
  Q=(4,4)
  PQ=√[(16-4)^2+(-8-4)^2]
  PQ=√(144+144)
  PQ=12√2 SQ.UNITS
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question asks to show that the line \(X + Y = 8\) intersects the parabola \(y^2 = 4x\) at two points \(P\) and \(Q\), and to find the coordinates of these points, the equation of the chord \(PQ\), and its length. The answer provides a detailed step-by-step solution to the problem.
  
  Label: question-and-answer