how to parametrize 1 Attachment(s) I need to know how I can parametrize please. If I can learn this I can do the others. 
I am able to parametrize a plane now. so disregard the plane part please. and now still watching video classes :) 
you can rewrite the quadric surface as $4x^2 + 3z^2 = 1+2y^2$ and parameterize it as $(2\sqrt{1+2y^2} \cos(\theta),~y,~\sqrt{3(1+2y^2)} \sin(\theta)),~y\in \mathbb{R},~0 \leq \theta < 2\pi$ 
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$\pi$. 
Since I don't know anything about how to parametrize a surface I did not understand anything from the answer :( 
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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 
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 
Obtaining parametric equations for a plane (such as 3x  z = 6y + 3) is explained in detail in this article. 
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