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Questions tagged [parametric]

For questions about parametric equations, their application, equivalence to other equation types and definition.

In mathematics, a parametric equation of a curve is a representation of this curve through equations expressing the coordinates of the points of the curve as functions of a variable called a parameter. This contrasts with implicit equations that define a curve as the zero set of some equation in the coordinates.

The parametric forms of curves are well-suited for drawing on a computer, while their corresponding implicit forms are useful for analytic manipulations (intersections, etc.)

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Find the points where the curve $r(t) = \langle{t, t^2, t^3\rangle}$ intersects the surface $zx = 13y - 36$

1) Rearrange the equation to : 13y - zx = 36 2) To find the point of intersection, we plug the parametric equations into equation for the plane; 13 (t^2) - 1(t^3) x 1(t) = 36 13t^2 - ( t^3 x t ) = 36 13t^2 - ( t^4 ) = 36 t^2 ( 13 - t^2 ) = 36 13 -…
Priscilla Naraine
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With reference to Figure Q3, write parametric functions $x (u), y (u), u \in [0, 1]$ defining this spiral curve.

I am having a hard time trying to figure this out: U domain is [0,1] []1
mathsmad
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The parametric form of a line

For the parametric representation of a line L with the following points, is my answer correct: P1 = <2,2,0>, P2 = <0,-2,-4>, P3 = <3,4,2> Is this correct: X = P1 + s.P1P2 + t.P1P3 = <2,2,0> + s.<-2,-4,-4> + t.<1,2,2>?
nsc010
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Convert function $\ x^4 - y^4 = xy$ to a parametric form

I can't figure out how to convert this function to parametric form. $$\ x^4 - y^4 = xy$$ $$\ x(t) =? $$ $$\ y(t) =? $$ Any help would be greatly appreciated. Thanks!
Anmol
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Defining Parametric function for a plane passing through points

Question: Propose how to define parametrically with functions x(u,v), y(u,v), z(u,v) a plane passing through points with coordinates (-4,0,0), (0,4,0), (2,0,4). My thought process would be to use a bilinear representation to define the middle…
arc2test
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Question about the sketch of a parametric curve

The problem is so sketch the curve parametrized by $x = \sqrt{t}$ and $y = t-5$. Solving, I get that $t = x^2$ and so $y = x^2 - 5$. In the solutions of my textbook, the graph is only drawn for $x \geq 0$ (the half of the parabola that lies to the…
mXdX
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How many solutions has this equation with a parameter?

How many solutions has an equation $$|x-1|+|x-2|+|x-3|+...+|x-2002|=a$$depending on an a parameter? In my opinion, an equation can have 0, 2 or infinite number solutions, but I don't know how to prove it.
user678243
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Eliminating parameter

How do you solve for "$t$" in either equation to eliminate the parameter and solve in terms of $x$ and $y$? $$ \begin{split} x&=\frac{ 1+t }{ \sqrt{1+t^2}}\\ \\ y &= \frac{1-t}{\sqrt{1+t^2}} \end{split} $$
Jared
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Parametric equation for y^2 = x+1

How do you parametrise $$y^2 = x+1$$ ? I only know how to parametrise a circle.
Dovendyr
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Angle of ellipse's long axis and abscisa

I am reading a paper where I encountered the following equations $x=a.\cos(\omega t)$ and $y=b.\cos(\omega t + \phi)$ $\phi$ and $\omega$ are constants, t is the variable parameter. Then the paper suggests this is the parametric equation of an…
AWally
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Finding equation of a curve that a parametric equation of a line is tangent to

I have the line $y=x\cdot\frac{-a}{-3a^2+4}$. I want to find the curve that this line is tangent to. More info: the tangency point needs to be at coordinates $(\frac{a\left(-3a^2+4\right)}{-9a^2+16},-\frac{a^2}{-9a^2+16})$ Clarifications: The line…
TreasureGhost
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toroidal knot patch/ribbon

I know I can create a toroidal knot ribbon: If B is the binormal to the curve, adding uB to the parametrization for some u between -1 and 1 should do it. You get a surface described by r(t,u). However, this ribbon will always be tangent to the…
adam.hendry
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How do I eliminate the element 't' from two given parametric equations?

I'm stuck with this, and would appreciate if someone could guide me through it as I can't really take the exercise further without this knowledge. I have two parametric equations (they represent the parametric equations of a points movement): x =…
Edward B
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Find the points on the curve where the tangent is horizontal or vertical: $x= e^{\sin(t)}$ ;$ y= e^{\cos(t)}$

What I understand is that where the t-value of $\frac{dy}{dt}$ and $\frac{dx}{dt}$ is equal to $0$, you can use that $t$ to determine the $x$ and $y$ coordinates of the point. What I got for my vertical tangent was $(e,1)$ and horizontal $(1,e)$…
dan
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Showing a point on a Cartesian plane also lies on a line

I'm just doing some revision for an upcoming exam. Our lecturer has given us problems with solutions to help study for the exam. I've come across a problem which i don't understand. Question: Given the line , L1= (x,y) = (-1,-4) + (8,24)t Show that…
Lui H
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