# 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!
The text passage contains a mathematical question and its answer, specifically about finding the slope of the line between two points where the graphs of two sets of parametric equations intersect.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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!
user
The text passage contains a mathematical question and its answer, specifically about finding the slope of the line between two points where the graphs of two sets of parametric equations intersect.

TYPE: SINGLE_QUESTION_WITH_ANSWER