# Tagged Questions

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### Parametric & Trigonometry

$$x=7\sin(t)+\sin(7t)$$ $$y=7\cos(t)+\cos(7t)$$ How would I solve this one out? I have to simplify the two enough to graph it. I squaring the two and adding them together, but I hit a roadblock: ...
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### Parametric Equations

$x=3\sin^3t$ $y=3\cos^3t$ How would I even begin to work out this one? I'm supposed to graph it, but I have no clue what how to even start it.
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### Showing that these two lines are parallel.

$$\dfrac{x - 1}{2} = 2 - y = 5 - z \quad \text{and} \quad \dfrac{4 - x}{4} = \dfrac{3 + y}{2} = \dfrac{5 + z}{2}.$$ I was given this math problem as homework, and I have spent the past hour ...
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### Find all values of $a$ for which there are two real solutions of $x^3-2ax^2+a^2x-3=0$

Find all values of $a$ for which there are two real solutions of the equation. $$x^3-2ax^2+a^2x-3=0$$ Ans = $1.5\sqrt[3]{6}$ I tried to research the function by dint of derivative, but it didn't ...
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### Find Vector and Parametric Equation

I'm having some trouble finding answers to these problems. When i try to find help online, all i find are (x,y,z) problems and I'm simply looking for a PreCalculus (x,y) problem solving technique: ...
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### Parameterisation Q

I'm looking to parameterise the expression $$f(r,\theta)=Usin(\theta-\alpha)(r-\frac{a^2}{r})-\frac{\Gamma}{2\pi}lnr-k=0$$ s.t. $z=re^{i\theta}$. I get a horrible expression if I parameterise for r. ...
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### Show that the equation of the folium of Descartes in terms of $x$ and $y$ is $x^3+y^3=axy$

I'm given that the parametric equations are $x=\frac{at}{1+t^3}$ and $y=\frac{at^2}{1+t^3}$ and that $a>0$ Here's my attempt at a solution: Find $x^3$ and $y^3$ in terms of $t$.. ...
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### calculate velocity using parametric functions

if i have the following parametric functions where time is m/s : x = 8 t y = -5 t2 + 6 t and i want to find the initial velocity can i do the following: ...
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### What is parametrics and Parametrization of equations?

I always read about parametric equations and parametrization of equations, but what is that anyway? how can I tell the difference between a Parametric equation and a 'normal' one?
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### Parametrizing a given line and equations

1) Parametrizethe given line contraining the points (3,2) and (-5,6). 2) Find the parametric equations for the segment joining the given points (2,3) and (5,5) where $0\leq t \leq 1$. ...
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### 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 ...
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### 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 $t$?
Write each pair of equations as a single equation in $x$ and $y$. a)$\begin{cases} x=t+1 &\\ y=t^2-t & \\ \end{cases}$ b)$\begin{cases} x=\sqrt[3]{t}-1 &\\ ... 1answer 640 views ### Using Parametric Equations to Define the Position of an Object in Motion What is the intuition behind the equations for the parametric equation applications below? Rather than memorize the formulas for a quiz i'd like to gain a deep understanding of them. 1answer 97 views ### Parametric equation involving exponents and e How do you go about solving this problem? For each plane curve given below, find a rectangular equation. State the appropritate interval for$x$and$y$.$x(t) = e^{5t}$,$y(t) = e^t$,$t \in ...
I'm trying to find the value(s) of the parameter $t$ at the intersection point(s) between a 2D general parabola (as a parametric function of $t$) and a line whose equations can be derived from two ...