Mathematics Stack Exchange
Mathematics Stack Exchange

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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Question about second derivatives of parametric equations?

Consider the parametric curve given by $$x=4+t^2,\, y=−10t^2−10t^3$$ For $\dfrac{dy}{dx}$, I found $-5(2+3t)$ For $\dfrac{d^2y}{dx^2}$, I keep getting $\dfrac{d}{dt}\dfrac{-5(2+3t)}{2t} = \dfrac{-15}{2t}$ It's wrong! Why? The answer is supposed to…
Kris
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Finding the points of a paramertized curve where a tangent line has slope 3?

I have a curve at $c(t) = (-5t^2-3t+4,t^3-9t+5)$ and given a slope for the tangent line of $3$. I would like to find the point $(x,y)$ where this occurs. What I did is took the derivatives of $x(t)$ and $y(t)$, came up with an equation for the…
Michael
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Parametrization for the curve on cylinder $y = 7 - x^4$ that passes through the point $(0, 7, -3) $when t = 0 and is parallel to the xy-plane

Can you help me? So far I have turned $y = 7-x^4$ into $\langle1, 1, 0\rangle$ and used it to make the equation $L = (0, 7, -3) + t(1, 1, 0)$. I know this is wrong, but I just don't know what, and I know it has to do with $y = 7-x^4$. Thank you in…
anon12345
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Eliminating the parameters of a cycloid

I was given two parametric equations and I need to eliminate the parameters, but I have no idea how. That pesky $\theta$ is hard to get rid of. Any suggestions? I tried many trig identities $x$ = $\theta$ - sin $\theta$ $y$ = 1 - cos $\theta$
sirferrum
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Converting parametric equations in a numerical equation

Is it possible convert this parametric equations in a numerical equation? $$ \begin{cases} \displaystyle x(t)=tv_0\cos(\theta)\\ \displaystyle y(t)=tv_0\sin(\theta)-\frac{1}{2}gt^2+h \end{cases} $$ Look at this Wikipedia's entry, at: "Conversion…
Aurelius
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What is the implicit form of $x=cos(t),y=-3+cos(2t)$?

I know I have to use the properties of the trigonometric functions but I don't know which of them would help me get the answer.
Nicolás Siplis
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Parametric equations of a line

"Find the parametric equations of a line that passes through point $(1,1,0)$, parallel to plane $2x+3y+z=7$ and perpendicular to the line $\frac{x-1}{-2}= \frac{y}{3}=-z-2$" I don't know where to start, I know how to find the equations when given…
Nicolás Siplis
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Rational parametric equation graphing

Sketch the parametric equation on the Cartesian plane
Soren Lorensen
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Parametric Equation - need help

I was wonder if anyone would be able to help me with this problem. I have done problems similar but the +3 is throwing me off in this problem. How would you make it into a rectangular equation? equation
apknusel
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use the Parameterization in u and v to write the term $x^2+y^2$

Given that : $u=xy$ $v=x^2-y^2$ we want to write the term $x^2+y^2 $ using only $u$ and $v$. how can we do this ? update: please reread my question I have edited it. I think it is clear now sorry for misconception
Waseem Francis
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