anonymous
  • anonymous
can someone explain to me parametric equations(calc2)
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
can you post afew examples?
anonymous
  • anonymous
given the curve x=t^2-t+2, y=t^3-3t find the points of horizontal and vertical tangency
anonymous
  • anonymous
think of t in seconds so equation 1 x=t^2-t+2 at t=5 x=25-5+2 x=18 with equation 2 you are y=t^3-3t y=125-15 =110 |dw:1332398497041:dw| im sure you get asked to change the two equations into 1

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anonymous
  • anonymous
why did you put in those values:t=5?
anonymous
  • anonymous
just trying to explain parameters
anonymous
  • anonymous
you then usually asked to express y in terms of x
anonymous
  • anonymous
but its asking to find the tangents. dont u do derivatives?and stuff?
anonymous
  • anonymous
yes
dumbcow
  • dumbcow
horizontal tangency, im guessing that means when dy/dx = 0 \[\frac{dy}{dx} = \frac{dy}{dt}*\frac{dt}{dx}\]
anonymous
  • anonymous
ya..
anonymous
  • anonymous
so once i have the derivative what do i do?
dumbcow
  • dumbcow
set it equal to zero and solve for t then plug in that t to get the (x,y) coordinates
anonymous
  • anonymous
plug the t into whre? the original?/
dumbcow
  • dumbcow
yeah , x(t) and y(t) that are given
dumbcow
  • dumbcow
you could find y(x) directly but i believe that would be more difficult here since you have a quadratic and cubic functions,
anonymous
  • anonymous
so in this example i get +-1 =t. then i get : x=2/4 y=-2,2 ya?
anonymous
  • anonymous
so the points of tangency are: 2,-2 and 4,2?
dumbcow
  • dumbcow
yeah thats what i get :) you could check on wolfram to verify
dumbcow
  • dumbcow
for vertical tangency, im not sure, that would basically be an asymptote so for what t values is the curve undefined
anonymous
  • anonymous
wait, but thats only for horizontal. for vertical the t=1/2. so you also get 7/4,-11/8
anonymous
  • anonymous
how do i check this answer on wolfram?
dumbcow
  • dumbcow
oh right, slope is undefined at t= 1/2 good job http://www.wolframalpha.com/input/?i=x+%3D+t^2+-t%2B2%2C+y+%3D+t^3+-3t
anonymous
  • anonymous
awesome. thatsthat all for that question.?im having a test and im so nerbvous cause i dont feel like we really focused on paramic euqations

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