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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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Parametric form of conical helix

Given a cone as \begin{array}{l} x=s\cos t\\ y=s\sin t\\ z=s\cot\alpha\end{array} How could I get parametric form of any conical helix? Thank you.
lilezek
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parametric equation of line 1 perpendicular to a plan

Hi I would like to find the parametric equation of the line L passing by P0 (the intersection of D1 and D2) and perpendicular to the plan having D1 and D2. D1 and D2 are others lines. I had to find the parametric equation of D1:\begin{cases} x…
Pierre-Luc Bolduc
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find a polar equation

$xy=7$ we get: $r(\cos(\theta)\sin(\theta))=7$ therefore the only logical equation that could possibly arise is: $r=\frac{7}{\cos(\theta)\sin(\theta)}$ yet web assign said nope $#%& off. Am I missing something basic here or is web assign dead…
K. Gibson
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Find a cartesian equation for the polar curve

given $r= 9 \tan(\theta)\sec(\theta)$ quite clearly we can do simple trig identities and make this much simpler to work with: Since: $\tan(\theta)= \frac{\sin(\theta)}{\cos(\theta)}$ and $\sec(\theta)= \frac{1}{\cos(\theta)}$ Using $x=r\cos(\theta)$…
K. Gibson
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Parametric Equations Problem

Im back! Um, i have a simple question im trying to get ready for test after 5 days.. I slacked of sadly :( on math, so i have to pick up my skills.. On my test review i have this question: The parametric equations of a vector are $x_t=3+5t$ and…
amanuel2
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finding cartesian equations of parametric equations

find the Cartesian equation for the parametric equation $$x=\frac{1}{\sqrt{1-t}} \text{ and } y=\frac{t}{1-t}$$ I tried cross multiplying but I cant seem to find the equation in terms of $t$ to substitute.
Tesha Caesar
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Parabola that intersects two lines and matching the slope of the two lines?

If I have two lines with equations;$$x=0$$ $$y=0$$ $$z=t$$ and $$x=t$$ $$y=10$$ $$z=t$$ are there any parabolas that cross through the two lines and in which the parabola matches the slope of the lines at the points of intersection?
Anders Gustafson
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Find angle of line and time of impact for a line between two parametric circles.

I am trying to find the angle of a parametric line so that it will intersect a circular parametric curve when both of their parameters are equal. I also need to have the line's start position be defined by another parametric curve. What I have so…
Nick DeFilippis
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Is this a correct parametrization of a rectangle on the complex plane?

$z = 3 + i(2t - 1), t \in [0,1) \\ z = 3 - 6(t-1) + i, t \in [1,2) \\ z = -3 + i(1 - 2(t-2)), t \in [2,3) \\ z = 6(t-3) - 3 - i, t \in [3,4]$ I parameterized a rectangle with vertices at (-3,-i),(-3,i),(3,i), and (3,-i) in the above manner. However,…
John Sawatzky
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Parametric equations - finding A

The curve with parametric equations x = a(t-2), y = at² + 2 (where a≠0), meets the y-axis at the point (0,5). (a) Find the value of the constant a. (b) Hence determine whether the curve meets the x-axis
tim wood
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Switching a non parametric equation to a parametric equation of a plane

More than the result (that I already have printed in my book), I'd be interested in the procedure to switch from a non parametric to a parametric equation of a plane in the Euclidean space. Here is the exercise: Find parametric equations describing…
ocram
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Finding the parametric equation for a longbow curve about a circle

In the figure the circle of radius $a$ is stationary, and for every $\theta$, the point $P$ is the midpoint of the segment $QR$. The curve traced out by $P$ for $0<\theta<\pi$ is called the longbow curve. Find the parametric equations for this…
codax
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Parametric Equation explanation

Explain how the expression $tX + (1-t)Y$, $0\le t\le 1$, produces a segment that connects point $X (x_1, y_1)$ with point $Y (x_2,y_2)$. So I rearranged the problem such that $t(X - Y) + Y$ which I gather the $(X-Y)$ to be changes in $x$ and $y$,…
Lindsey
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Is it possible to turn the parametric equation of a line in 3 dimensions into the general equation?

I Know it is impossible to do so since the parametric equation for a plane is the intersection of $2$ planes.For example: $x$ $=$ $\frac{-5}{4t}+\frac{1}{4}$; $y=\frac{3}{4t}+\frac{5}{4}$; $z=t$ But when I combine any of the 2 equations above, I…
JimfyWinsy
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Rearranging this equation

This is based on a parametric equation problem. We have two ships A and B at $(-2,at +1)$ and $(4, t+10)$ respectively. I need to show that $d^2 = (1-a)^2t^2 +18(1-a) t +117$ using the distance formula I have got: $d^2 = (4+2)^2 +((t+10) - (at…
Mathsguy9020
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