The parametric tag has no wiki summary.
2
votes
4answers
185 views
Parametrization for intersection of sphere and plane
Given is the sphere $x^2 + y^2 + z^2 = 4$ and the plane $x + y = 2$ in $\mathbb R^3 $.
How can I find a parametrization for the intersection of the two?
3
votes
1answer
148 views
How are the parametric equations describing the cupid curve derived? [duplicate]
No doubt as some people have already seen, today morning wolfram posted the best valentine ever. The graph depicting cupid with its arrow and floating hearts around it involves something like 6 pages ...
0
votes
1answer
212 views
Converting parametric equation to implicit form
So I have the equation defined in homogeneous coordinates $[w; x, y]$ as $[1+t^2; 1-t^2, 2t]$
$$w = 1+t^2$$
$$x = 1-t^2$$
$$y = 2t$$
If I do $w+x-y$ I get $-2t+2$, so $t = -(w+x-y-2)/2$. I was then ...
2
votes
2answers
34 views
Parameterized curve describing trajectory of thrown object
We describe the trajectory of a thrown object (neglecting friction and similiar effects) with the curve
$$k(t) = \left(v_0\cos(\beta)t,\,v_0\sin(\beta)t-\frac{g}{2}t^2\right)$$
with ...
1
vote
1answer
66 views
Domain of parametric equation
If there is a parametric equation $x=2\cos{2t}$ and $y=6\sin{t}$, $0\le t \le \frac{\pi}{2}$ the Cartesian equation is $y=3\sqrt{2-x}$.
How do I find the domain of the Cartesian equation?
I tried:
...
3
votes
2answers
116 views
Plotting parametric equations in gnuplot
I am trying to plot the following parametric equation in gnuplot:
fx(t) = -35*cos(t) + 65*cos(-.35*t)
...
2
votes
0answers
176 views
Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?
I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly.
I know
$$\nabla\times E= ...
0
votes
1answer
92 views
equation for the region inside a circle
What equation or group of equations fill the entire or part of a region inside a circle without using inequalities?
Update
I don't know if this problem is already solved, I'm trying to find the ...
1
vote
2answers
110 views
Understanding cubic bezier curve
I do not have experience of Mathematics past a-level, so please excuse the incorrect terminology.
I am trying to better understand the fundamentals of how a cubic bezier curve works. I am going by ...
0
votes
2answers
34 views
what's the algebra (if any) behind converting f(x) for a circle to a parametric equation
I'm sure there has to be some algebra behind it. My problem called to covert
$$(x - 2)^2 + (y - 9)^2 = 4$$
if $x = 2 + 2cos(t)$
then $y = ? $
I know the answer is $9 + 2\sin(t)$ but I simply got ...
2
votes
2answers
107 views
parametric curves, parameter and integration
I just started learning about parametric curves and I find it confusing that we have a 3rd variable but this 3rd variable "t" is some imaginary variable....I dont get what the difference is between ...
4
votes
3answers
267 views
Writing Polar Equations In Parametric Form
For an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function $r=2\cos 3\theta$, and re-wrote it ...
2
votes
1answer
62 views
Parametric Equation of a Circle Using a Line
Consider the unit circle
$$
x^2+y^2=1.
$$
How can I parametrize it using the line $y=m(x+1)$, where $m$ is its slope?
0
votes
1answer
59 views
Help me understand a surface integral question?
The question is:
Evaluate the surface integral:
$$
\iint\limits_S \, x^2yz\ \mathrm{d} S
$$
Where S is part of the plane z = 1 + 2x + 3y that lies above the rectangle [0,3] X [0,2]
I literally just ...
2
votes
1answer
88 views
Finding parametric equations
I am trying to understand volume and surface integrals. I do get the idea of the process (find a parametric equation of the volume/surface, integrate afterwards). But I just cannot make up parametric ...
0
votes
0answers
79 views
Finding parametric equations
I am trying to understand volume and surface integrals. I do get the idea of the process (find a parametric equation of the volume/surface, integrate afterwards). But I just cannot make up parametric ...
1
vote
1answer
82 views
Find the Frenet frame
Consider the following space curve:
$$ \gamma(x)=(e^x\cos(x), e^x\sin(x), e^x). $$
My main goal is to find the Frenet Frame T,N,B.
So far I have found the arc-length using the following formula:
$$ ...
3
votes
2answers
145 views
Converting $x=\frac{1}{2}\cos\theta\;;\;\; y=2\sin\theta $ to Cartesian form
How can we transform these parametric equations to Cartesian form?
$x=\frac{1}{2} \cos\theta, \quad y=2\sin\theta \quad\text{ for}\;\;0 \leq \theta \leq \pi$
2
votes
2answers
55 views
Converting $x = \sin \frac{t}{2}, y = \cos \frac{t}{2}$ to Cartesian form
How can we transform these parametric equations to Cartesian form?
$$x = \sin \frac{t}{2}, \quad y = \cos \frac{t}{2}, \quad -\pi \leq t \leq \pi.$$
0
votes
3answers
70 views
Help me to sketch this parametric curves
Is there any defined process to sketch parametric curves?
Thanks in advance.
$$x = \cos^2 t, \quad y = 1 - \sin t, \quad 0 \leq t \leq 2\pi.$$
1
vote
1answer
47 views
Find a function f(x) such that the parametric curve could be obtained by flipping the graph
Find a function f(x) such that the parametric curve could be obtained by flipping the graph of f across the line with slope 1 that goes through the origin.
parametric curve with coordinates (t^14, ...
1
vote
3answers
109 views
How do we prove that two parametric equations are drawing the same thing?
For example, if I have
$$\begin {align}
x(t) &= r\sin t\cos t\\
y(t) &= r\sin^2 t\\
\end {align}$$
and
$$\begin {align}
x(t) &= \frac r 2 \cos t\\
y(t) &= \frac r 2 (\sin t + 1)
...
0
votes
1answer
115 views
Arc Length Of Parametric Curve
I attached the problem as a file:
Where did the trig functions go? I sifted through the different trig identities and formulas, but couldn't find anything that I could use. What should I do?
2
votes
2answers
595 views
Finding Where A Parametric Curve Intersects Itself
The problem I am working on is to find the where the curve intersects itself, using the parametric equations.
These are: $x=t^2-t$ and $y=t^3-3t-1$
For the graph to intersect itself, there must be ...
2
votes
1answer
665 views
Finding Where A Parametric Curve Crosses Itself
The parametric functions I am dealing with are: $x=2\sin2t$ and $y=3\sin t$
I know for a parametric graph to cross itself, there must be two distinct $t$, $t_1$ and $t_2$, that when placed into the ...
1
vote
1answer
196 views
Finding Parametric Equations For A Rectangular Equation
I am trying to find a general way of finding parametric equations for a rectangular equation.
The problem I am working on is $y=x^3$, and I have to find two examples of parametric equations. ...
1
vote
2answers
99 views
Parametric Equation Problem
The problem is, "to determine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain."
(a) $x=t;\quad ...
1
vote
1answer
62 views
Restriction Of Parametric Functions Domain
The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by
eliminating the ...
0
votes
2answers
31 views
Need help with this parametric equation
$s(t)=(\frac{2}{t^2+1},\frac{2t}{t^2+1})$
I need to calculate a line integral along this path. But I have trouble understanding what it is. I did some googling and it looks that it is a parabola, but ...
0
votes
2answers
37 views
How do I find the 2 slopes at which this parametric function crosses itself?
I have a parametric function. If you graph it, you'll find that it looks like a figure 8.
x(t) = 2sin(2t)
y(t) = 8sin(t)
How do I find the slopes of the function ...
1
vote
1answer
251 views
Parametric equation of a cone
I usually use the following parametric equation to find the surface area of a regular cone $z=\sqrt{x^2+y^2}$:
$$x=r\cos\theta$$
$$y=r\sin\theta$$
$$z=r$$
And make $0\leq r \leq 2\pi$, $0 \leq \theta ...
0
votes
0answers
63 views
complex circular motion
Assume the planet orbits its star in a circular orbit of 100 units with period 360 days. The moon in turn orbits its planet at a radius of 10 units and period 28 days. Finally the moon rotating, we ...
4
votes
1answer
69 views
Can (x(t), y(t)) generate a surface? If so, can the surface be continuous?
Intuitively, the parametric equation $z = (x(t), y(t))$ seems to only be able to generate one-dimensional objects, i.e. curves.
However...
Let $x(t)$ be "the odd-indexed digits of the real number ...
2
votes
2answers
86 views
Parameter values that make function values side lengths of a triangle
I have been trying to solve the following problem for more than a week without any success.
Given the function:
$$f(x)=\frac{x^2+mx+4}{x^2+x+4}$$
Find all possible values of the parameter $m$ such ...
1
vote
1answer
55 views
How can I re-write an equation (or system of equations) in parametric form?
For the equation $y = 3x$ I need to re-write $x$ and $y$ in terms of a variable $t$. How can I find the value of each variable in terms of $t$?
2
votes
1answer
73 views
How to find a parametric equation?
I want to find an equation for a race track, so I could get the position of a point with respect to time. Let's say I have this track and here are a few points on it:
Could it be possible to model ...
0
votes
1answer
56 views
parametrizing quarter of a circle
I am given the circle whose equation is: $(x-\frac{1}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{1}{2}$. So, the coordinates of the origin of the circle are: $(\frac{1}{2},-\frac{1}{2})$ and the radius of the ...
1
vote
1answer
141 views
converting a parametric R5 vector into a Cartesian form
How do you solve a problem like this. I'm completely stumped. it seems like there should be an easy solution but I'm obviously over looking it. any help would be greatly appreciated.
2
votes
2answers
78 views
Constant velocity of a sine function
I am defining the location of an object based on the sine function. The position of the object at s seconds along the x-axis is defined as x=s and its position along the y-axis is defined as y=sin(x). ...
0
votes
1answer
221 views
Find the area bounded by the parametric curve…
Find the area bounded by the parametric curve $x = \cos(t)$, $y = e^t, 0 < t < \pi/2$, and the lines $y = 1$ and $x = 0$.
I do not even know where to start with this problem. I know that I need ...
2
votes
3answers
1k views
How to find a parametric equation for the tangent line to the curve of intersection of the cylinders?
How can i find a parametric equation for the tangent line to the curve of intersection of the cylinders $x^2 + y^2 = 4$ and and $x^2 + z^2 = 1$ at the point $P_0(1,\sqrt{3}, 0)$?
0
votes
1answer
78 views
How do we find the length of the line (parametric curve)?
A curve in the $xy$-plane is given parametrically by
$$x(t) = e^{2t}, \quad y(t) = e^{2t} \sin(2t), \quad t \in [0, \pi/2].$$
What is the length of this curve?
Ok, actually I know what to do, ...
0
votes
1answer
61 views
Converting parametric equations in a numerical equation
Is it possible convert this parametric equations in a numerical equation?
$$
\begin{cases}
\displaystyle x(t)=tv_0\cos(\theta)\\
\displaystyle y(t)=tv_0\sin(\theta)-\frac{1}{2}gt^2+h
\end{cases}
$$
...
1
vote
0answers
41 views
Maximum value for parameter
I am facing the following problem:
A number of a adults, b children older than 12, and c children younger than twelve attend an event. The sum of all people a+b+c=100. The prices are \$6 per adult, ...
1
vote
1answer
783 views
Equation for making a circle in 3D space
I have a 3D space with axis $(x, y ,z)$ and I can make a circle in the $xy$-plane.
To make a circle in the xy-plane I currently use spherical coordinates $(r, \theta, \phi)$ where $r = 1$, $\theta = ...
1
vote
1answer
207 views
Parameterize a straight line using polar coordinates… without angle.
I had to parameterize a straight line with starting point in $A=(-3,7)\\ $ and endpoint in $B=(4,1)$.
My idea was to use the equation for the line that goes through two points. That is:
$$
\frac { ...
1
vote
1answer
73 views
Parametric Equation of a Particle Movement inside a Vortex in a Rectangular Box
I am trying to simulate the movement of a particle in a vortex in a rectangular box, I am currently using an ellipse but that causes the particle to collide with the walls more that I want.
The ...
1
vote
2answers
101 views
Finding Tangent line from Parametric
I need to find an equation of the tangent line to the curve $x=5+t^2-t$, $y=t^2+5$ at the point $(5,6)$.
Setting $x=5$ and $y = 6$ and solving for $t$ gives me $t=0,1,-1$. I know I have to do ...
1
vote
1answer
376 views
Parametric Equation
Let $P_1$ be the plane through the origin containing the vectors $[1,2,-1]$ and $[0,1,1]$. Let $P_2$ be the plane through the point $(1,1,1)$ parallel to the vectors $[-1,2,2]$ and $[3,4,-2]$
I know ...
0
votes
1answer
31 views
Represent sorting position by a parametric form
Given a set of random integers {0,5,100,65,...,0,1,2}, is there a mathematical method existing to construct a parametric form $f$ (the number of parameters $<<$ the number of integers) so that ...
