Results 1 to 4 of 4

Math Help - Conics, Parametric Equations, & Polar Coordinates

  1. #1
    Junior Member
    Joined
    May 2007
    Posts
    69

    Conics, Parametric Equations, & Polar Coordinates

    I have no clue how to do these problems! Could someone help please??
    Thanks.

    1) Sketch the curve represented by the following parametric equations ( indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.

    a) x= 2t^(2), y= t^(4) + 1

    b) x= t^(2)+ t, y= t^(2) - t

    c) x= e^(-t), y= e^(2t) - 1`

    d) x= 4 + 2 cos Theta

    e) x= 4 sec Theta, y= 3 tan Theta

    2) Use a graphing utility to graph the curve represented by the following parametric equation. Indicate the direction the curve. Identify any points at which the curve is not smooth.

    a) Witch of Agnesi: x= 2 cot Theta, y= 2 sin^(2) theta
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by googoogaga View Post
    1) Sketch the curve represented by the following parametric equations ( indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.

    a) x= 2t^(2), y= t^(4) + 1
    Let's take this one for example.
    To plot it simply choose a number of t values, say -2 \leq t \leq 2. (You may wish to use a calculator.) This will give you a series of (x, y) points, which you can connect with a smooth curve.

    To get an equation for y you need to "eliminate the parameter" t from the equations:
    x = 2t^2 \implies t = \sqrt{\frac{x}{2}}

    Thus
    y = t^4 + 1 = \left ( \sqrt{\frac{x}{2}} \right )^4 + 1 = \frac{x^2}{4} + 1

    So this appears to be a parabola.

    -Dan
    Last edited by topsquark; September 13th 2007 at 07:04 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2007
    Posts
    69

    Conics, Parametric Equations E& Polar Coordinates

    How would you solve exercices c and e and 2) a? There are some algebraic rules that I am not really remembering
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    c) \displaystyle x=e^{-t}=\frac{1}{e^t}\Rightarrow e^t=\frac{1}{x}.
    \displaystyle y=e^{2t}-1=(e^t)^2-1\Rightarrow y=\frac{1}{x^2}-1.

    e) \displaystyle x=\frac{4}{\cos\theta}\Rightarrow x^2=\frac{16}{\cos^2\theta}=16(\tan^2\theta+1).
    Then \displaystyle x^2=16\left(\frac{y^2}{9}+16\right)\Rightarrow\fra  c{x^2}{256}-\frac{y^2}{144}=1
    which is a hyperbola.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. coordinates of P - parametric equations
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 14th 2009, 03:48 PM
  2. Equations in Polar Coordinates
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 6th 2009, 10:04 PM
  3. Converting polar equations to parametric
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 26th 2007, 05:48 PM
  4. Replies: 2
    Last Post: August 28th 2007, 02:55 PM
  5. Parametric / polar equations
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: March 4th 2007, 11:49 PM

Search Tags


/mathhelpforum @mathhelpforum