September 15th, 2018, 12:43 PM  #1 
Senior Member Joined: Apr 2017 From: New York Posts: 119 Thanks: 6  how to parametrize
I need to know how I can parametrize please. If I can learn this I can do the others. 
September 15th, 2018, 01:31 PM  #2 
Senior Member Joined: Apr 2017 From: New York Posts: 119 Thanks: 6 
I am able to parametrize a plane now. so disregard the plane part please. and now still watching video classes 
September 15th, 2018, 10:58 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,307 Thanks: 1221 
you can rewrite the quadric surface as $4x^2 + 3z^2 = 1+2y^2$ and parameterize it as $(2\sqrt{1+2y^2} \cos(\theta),~y,~\sqrt{3(1+2y^2)} \sin(\theta)),~y\in \mathbb{R},~0 \leq \theta < 2\pi$ 
September 16th, 2018, 06:05 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,281 Thanks: 1965 
Unfortunately, the coefficients aren't quite right in romsek's answer and the equation used was incorrect (it should have been $4x^2 + 3z^2 = 2y^2  1$). Corrected (and using ±(1/√2)cosh(u) instead of y), one gets ((1/2)sinh(u)cos(θ), ±(1/√2)cosh(u), (1/√3)sinh(u)sin(θ)), u $\small\geqslant$ 0, 0 $\small\leqslant$ θ < 2$\pi$. 
September 16th, 2018, 05:34 PM  #5 
Senior Member Joined: Apr 2017 From: New York Posts: 119 Thanks: 6 
Since I don't know anything about how to parametrize a surface I did not understand anything from the answer 
September 16th, 2018, 06:37 PM  #6  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,041 Thanks: 815 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
So all we are doing is finding a way to "cut down" on the number of variables we need to trace out a solution. (Or alternately, put the equation into a form that is simpler to work with.) Dan Last edited by skipjack; September 17th, 2018 at 12:06 AM.  
September 16th, 2018, 07:31 PM  #7 
Senior Member Joined: Apr 2017 From: New York Posts: 119 Thanks: 6 
for circle yes x= rcos(Theta) y=rsin(Theta) what about 3xz=6y+3 or 2y^23z^2=1+4x^2 need to learn before test 
September 17th, 2018, 12:19 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,281 Thanks: 1965 
Obtaining parametric equations for a plane (such as 3x  z = 6y + 3) is explained in detail in this article.

September 17th, 2018, 07:50 AM  #9  
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124  Quote:
 

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