# Questions tagged [parametrization]

For questions on parametrization, the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.

673 questions
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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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### Parametric equation of a rose with $5$ petals, orthogonal to $x+y+z=3$, with radius $4$, center $(1,1,1)$, and a petal in the direction of $(0,0,3)$

I am kind of stuck in this exercise. Write the parametric equation of a rose-shaped curve with 5 petals, radius 4, centered on $(1,1,1)$, orthogonal to the plane $x+y+z=3$, such ...
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### Finding parametrization of the curve of intersection

Given 2 equations $z = x^2 - y^2$ and $z = x^2 +xy -1$, find a parametrization of the curve of the intersection of the surfaces. By equating them together, I get $y^2 +xy -1 =0$. Letting $x=t$, I ...
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### Continuous paths joining positive x-axis to negative x-axis, through upper half plane

I need a way to parametrise all continuous paths from the positive to the negative x-axis, which go through the upper half plane (in $2$ dimensions). I do not care about the speed of the ...
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### parametrization of a moving wheel

Attempt: Given, radius of wheel $0.5 m$ Total distance travelled by the point during first revolution = circumference of the wheel therefore, distance travelled by the point $2 \pi r$ where r is ...
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### Difference between a parametrized surface and manifold

What is the difference between a parametrized surface and manifold? Is it true that if $M \subset \mathbb R^n$ is an $n$-dimensional parametrized surface it is also a (parametrized?) manifold? I am ...
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### Parameterize $3x^2 + 4xy + 3y^2 = x+3y$

I am calculating the curve that is formed by the graph between the function $$f(x,y)=3x^2+4xy+y^2$$ and the plane $$z=x+3y$$ Then I'm left with the equation $3x^2+4xy+y^2=x+3y$ that I want to ...
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### Compute $\int_{\Gamma}\omega$ where $\omega=(y-2z)dx+(x-z)dy+(2x-y)dz$

Compute $\int_{\Gamma}\omega$ where $\omega=(y-2z)dx+(x-z)dy+(2x-y)dz$ and $\Gamma$ is the intersection between: $x^2+y^2+z^2=r^2$ and $x-y+z=0$ My attempt: $\Gamma$ is some kind of ellipse in the ...
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### Calculate $\int_{\Gamma} \omega$ when $\omega =z(z-y)dx+xzdy-xydz$, $\Gamma=\Gamma_1 \cup \Gamma_2 \cup \Gamma_3$

Calculate $\int_{\Gamma} \omega$ when $\omega =z(z-y)dx+xzdy-xydz$ $\Gamma=\Gamma_1 \cup \Gamma_2 \cup \Gamma_3$ $$x^2+y^2=(z-1)^2$$ $x\geq0, y\geq0,z\geq0$ $\Gamma_{1,2,3}$ are ...