0
votes
4answers
40 views

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 ...
0
votes
3answers
76 views

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 ...
0
votes
2answers
83 views

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: ...
1
vote
0answers
18 views

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. ...
0
votes
2answers
187 views

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 $t$.. ...
0
votes
2answers
75 views

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: ...
1
vote
1answer
65 views

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?
5
votes
2answers
158 views

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 $0\leq t \leq 1$. ...
2
votes
1answer
1k views

Find the cartesian equation of: $y = \sin (2t)$ and $x = \cos (t)$

$\eqalign{ & y = \sin (2t) \cr & x = \cos (t) \cr} $ therefore: $\eqalign{ & \sin (t) = {y \over {2\cos t}} \cr as: & \cos (t) = x \cr & {\rm{ sin(t) = }}{y \over ...
1
vote
4answers
348 views

Some general question about parametric equations

My textbook doesn't explain this very well, what I want to know is the purpose of parametric equations, what is a parameter? what is the advantage of these equations over a function y=f(x), what do ...
3
votes
2answers
97 views

Having trouble solving question involving parametric equations

I have been given the following: $$y = a \cdot \cos^3t$$ $$x = a \cdot \sin^3t$$ $$0 \leqslant t \leqslant {\frac\pi2}$$ I am supposed to show that the mean value of $y$ over the interval ...
4
votes
3answers
2k 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 ...
1
vote
1answer
64 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
1answer
222 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
2k 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
2k 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
1k 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
243 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
141 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 ...
1
vote
1answer
140 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 $t$?
1
vote
3answers
499 views

Write each pair of equations as a single equation in $x$ and $y$.

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 &\\ ...
1
vote
1answer
629 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.
1
vote
1answer
95 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 ...
2
votes
1answer
578 views

Find intersection(s) between parametrized parabola and a line

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 ...