# Questions tagged [parametric]

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

1,796 questions
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### Deriving logarithmic spiral equation from square corners

This is an interesting problem but I haven't been able to work it out (from Bender and Orszag, prob: 1.27) - any insight/assistance would be appreciated: Four caterpillars, initially at rest at the ...
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### Determining if 2 variances are equal with a rule of thumb?

So yes I am familiar with the F-test and know how to use it. Though I remember there was a quick rule of thumb of determine if 2 variances are equal. By either subtracting or dividing the 2 and it ...
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### Non-dimensionalize - Determine the dimensions of the parameters

I have the following assignment, I've made most of the assignment, but cannot seem to figure the rest out. The assignment: "Certain organisms have an effective growth, $\frac{\dot{n}}{n}$. A model ...
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### Skewed conical spiral equation

I'm struggling to find a formula for a spiral tracing a skewed cone. I need to generate x, y, z coordinates. Wolfram alpha has parametric equations for a conical spiral: http://mathworld.wolfram.com/...
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### System of linear equations with parameter

I have this system of linear equations with parameter: $ax + 4y + z =0$ $2y + 3z = 1$ $3x -cz=-2$ What I did was to put those equations into a matrix and transform that matrix it into a ...
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### Finding cartesian equation of curve with parametric equations

A curve has parametric equations $x=a \sin(⁡t)+b \cos(⁡t)$ $y=a \cos⁡(t)-b \sin⁡(t)$ How do I eliminate t to find the Cartesian equation here? I've tried different weird approaches, i.e. squaring ...
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### find $\lim _ {y\rightarrow + \infty } \int _ { 1 } ^ { 2 } \frac { \ln ( x + y ) } { \ln \left(x^{2}+y^{2} \right) } d x$

I need to find $$\lim _ {y\rightarrow + \infty } \int _ { 1 } ^ { 2 } \frac { \ln ( x + y ) } { \ln \left(x^{2}+y^{2} \right) } d x$$ Any hints? PS. i tried to convert problem to solving improper ...
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### Calculate surface limited by curve

How to calculate the surface limited by the curve described with the two equations: $x = 3+cos(t)$ $y=4sin(t)$ The formula we use is the one shown below: $\int_a^b |y(t).x'(t)| \,dt$ Now I'm ...
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### Convert $x(t)=2t\sin{t}+2\cos{t}$, $y(t)=2\sin{t}-2t\cos{t}$ to a Cartesian equation

I need help to convert following parametric equation in Cartesian: $$x(t)=2t\sin{t}+2\cos{t}$$ $$y(t)=2\sin{t}-2t\cos{t}$$ I've tried squaring both equations and adding first to second ...
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### The prolate cycloid

A cycloid is given by the parametric equations: $x = 2 - \pi \cos(t)$ and $y = 2t - \pi \sin(t)$. The problem asks for the slope of the tangents on the cycloid at a point where the cycloid ...
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### How to eliminate $a$ from the parametric equations of a locus?

Stated question: The point T ($at^2$, $2at$) lies on the parabola $y^2=4ax$ and L is the point ($-a$, $2a$). M is the mid-point of TL. Find the equation of the locus of M as T moves on the parabola. ...
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### Find distance from line k given parametric equation of: $x=2+t, y=-3+2t, z=2-t, t\in\mathbb{R}$ from plane $\pi:2x+y+4z=0$.

My solution: $$2(2+t)+(-3+2t)+4(2-t)$$ $$4+2t-3+2t+8-4t$$ $$9=0$$ Contradiction, so no solutions, line and plane are parallel. Its first time where I have such an example where equation is ...
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### How to give a parameterisation of $u(x_0,y)=y$ in the form $\Gamma(s)$?

I am working to solve a PDE with the given initial condition $$u(x_0,y)=y$$ where $x_0$ is a constant. In order to solve the PDE I need to parameterise the curve in the form $\Gamma(s)$. I have ...
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### Calculating an area of parametric function with wolframalpha?

Using wolframalpha, how can I calculate an area between some parametric function like: $\begin{cases} x(t) = t^2 - t \\ y(t) = t^3\end{cases}$ and: some other function like: $y = x^2$ ? I've ...
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### Envelopes In Mathematics

How can I make sure that when we eliminate the parameter from the curve \begin{align*} F(t,x,y) &= 0 \\ \frac{\partial F}{\partial t}(t,x,y) &= 0\,, \end{align*} the equation obtained is the ...
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### How does one find a parameter representation for bounded region?

I need help with this question. I have been stuck at it for a few days. My main problem is how I use the curve $K_r$ to find the parametric representation. I have a curve $K_r$ in the $(x,y)$-plane ...
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### Supply and Demand Functions with Tax

I've been given the below supply and demand functions: $q^s(p)=50p~~~~~~q^d(p)=100(\frac{12}{p}-1)$ I've answered the first few questions, which include finding the equilibrium etc, and inverting ...