2
votes
3answers
84 views

Parametrization of $y^2 - x^2=1$

I have found parametrizations for the level curve $y^2-x^2=1$, however, I have a question regarding one of them. From the Pythagorean trigonometric identity $\cos^2 x + \sin^2 x =1$ we obtain ...
0
votes
1answer
363 views

Find Equation of a Perpendicular Line Going Through a Point

I have the following parametric equation for line g: $$ x=3t\land y=-7+5t\land z=2+2t $$ I have to find the equation of a line perpendicular to $g$ and going through point $Q(3,-2,4)$ which lies on ...
1
vote
2answers
245 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
144 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
142 views

Parametrization of a solid

Find a parametrization $\sigma : I \subseteq \mathbb{R}^3 \rightarrow \mathbb{R}^3$, with $I$ a parallelepiped, of $\lbrace (x,y,z) \in \mathbb{R}^3 : |z| \leq 4x^2 + 9y^2 \leq 1 \rbrace $.