Notations proofs analytic geometry

[Function]

Hello everyone

 

I'd like to know if following notations are correct, as first steps in order to get the canonical equations for a parabola, ellips and hyperbola:

 

Parabola

 

Given the focus [math]F\left(0,\frac{p}{2}\right)[/math] and directive [math]d\leftrightarrow y=\frac{-p}{2}[/math] of a parabola [math]\mathcal{P}[/math].

 

[math]\mathcal{P}:=\forall P(x,y):\left|PF\right|=d(P,d)[/math].

 

Ellips

 

Given the focusses [math]F_1\left(c,0\right)[/math] and [math]F_2\left(-c,0\right)[/math] of an ellips [math]\mathcal{E}[/math] with main axis [math]2a[/math].

 

[math]\mathcal{E}:=\forall P(x,y):\left|PF_1\right|+\left|PF_2\right|=2a[/math]

 

Hyperbola (same as ellips but with - instead of +)

 

Are these notations correct?

Edited December 7, 2013 by Function

[studiot]

Does the first part of of your parabola statement make sense?

 

" P₁ is the set of all P (xy) contained in P₁ "

 

I have used P₁ for your script P.

[Function]

Does the first part of of your parabola statement make sense?

 

" P₁ is the set of all P (xy) contained in P₁ "

 

I have used P₁ for your script P.

 

 

edited; is it now a correct notation?

Edited December 7, 2013 by Function