text: # Parametric Equations- Take 2
  
  • Dec 16th 2013, 03:56 PM
  orange
  Parametric Equations- Take 2
  The graph of the parametric equations
  
  http://data.artofproblemsolving.com/...630b98248f.gif
  
  meets the graph of the parametric equations
  
  http://data.artofproblemsolving.com/...db231f43c3.gif
  
  at two points. Find the slope of the line between these two points.
  
  So far, I tried equating x's and y's, but got
  
  cos(t) = 2+ 4cos(s)
  sin(t)= 3+ 4sin(s)
  
  How can I add those and continue from there? Thank you!
  • Dec 16th 2013, 04:26 PM
  SlipEternal
  Re: Parametric Equations- Take 2
  You are trying to find relationships between s and t. That is very difficult. Instead, try to find relationships between x and y. What do you get from $x^2+y^2$ (use the first parametric equation)? What about (x-2)^2+(y-3)^2 (use the second parametric equation)?
  • Dec 16th 2013, 04:36 PM
  orange
  Re: Parametric Equations- Take 2
  Thanks, Slip! Using the cos^2+sin^2=1 theorem I ended up with
  
  4 cos(s) = -7 -6 sin (s)
  
  So x= 2 + -7 - 6 sin(s)
  
  And adding that to the other equation, y=3+4sin(s), I ended up with
  
  6y + 4x = -2
  And from this I can get y= -2/3 x -1/3
  
  So is the slope -2/3? I took an intuitive approach and aren't 100% sure if I did it right
  • Dec 16th 2013, 04:41 PM
  SlipEternal
  Re: Parametric Equations- Take 2
  That is correct
  • Dec 16th 2013, 04:44 PM
  orange
  Re: Parametric Equations- Take 2
  Thanks again!
explanation: The document is a discussion thread from a math forum where a user named "orange" posts a question about parametric equations and another user named "SlipEternal" provides guidance and feedback. The initial post contains a math question, and the subsequent posts include the question and an answer.
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: # Parametric Equations- Take 2
  
  • Dec 16th 2013, 03:56 PM
  orange
  Parametric Equations- Take 2
  The graph of the parametric equations
  
  http://data.artofproblemsolving.com/...630b98248f.gif
  
  meets the graph of the parametric equations
  
  http://data.artofproblemsolving.com/...db231f43c3.gif
  
  at two points. Find the slope of the line between these two points.
  
  So far, I tried equating x's and y's, but got
  
  cos(t) = 2+ 4cos(s)
  sin(t)= 3+ 4sin(s)
  
  How can I add those and continue from there? Thank you!
  • Dec 16th 2013, 04:26 PM
  SlipEternal
  Re: Parametric Equations- Take 2
  You are trying to find relationships between s and t. That is very difficult. Instead, try to find relationships between x and y. What do you get from $x^2+y^2$ (use the first parametric equation)? What about (x-2)^2+(y-3)^2 (use the second parametric equation)?
  • Dec 16th 2013, 04:36 PM
  orange
  Re: Parametric Equations- Take 2
  Thanks, Slip! Using the cos^2+sin^2=1 theorem I ended up with
  
  4 cos(s) = -7 -6 sin (s)
  
  So x= 2 + -7 - 6 sin(s)
  
  And adding that to the other equation, y=3+4sin(s), I ended up with
  
  6y + 4x = -2
  And from this I can get y= -2/3 x -1/3
  
  So is the slope -2/3? I took an intuitive approach and aren't 100% sure if I did it right
  • Dec 16th 2013, 04:41 PM
  SlipEternal
  Re: Parametric Equations- Take 2
  That is correct
  • Dec 16th 2013, 04:44 PM
  orange
  Re: Parametric Equations- Take 2
  Thanks again!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a discussion thread from a math forum where a user named "orange" posts a question about parametric equations and another user named "SlipEternal" provides guidance and feedback. The initial post contains a math question, and the subsequent posts include the question and an answer.
  
  Label: question-and-answer