3D form will be how to draw this picture?

Question

3D form will be how to draw this picture? parabola, circle, ellipse and hyperbola 3D

Answer 1

Ok, since I remembered this question that has a "3D" cone already done we can steal the code there and that saves as half the trouble. In reality, the 2D drawing looks like this (when there's no perspective - \p=0):

Where the colored lines are planes cutting the cone. From Mark Wibrow's answer we can use the calculated \rx and \ry values to find the starting position of our hyperbola and parabola, and also define the bend coordinate of those. The important thing for perspective is that this bend is tangent to the cone edge, so we also calculate the tangency angle (which must be given as parameters for making the cone. At last, given some perpesctive (0<\p<1) to the previous drawing it looks like this:

MWE

% Most of the code is taken from https://tex.stackexchange.com/a/332015/81905
%Courtesy of Mark Wibrow
\documentclass[border=5]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[parabola/.style={very thin, red}, hyperbola/.style={very thin, violet}, circle/.style={very thin, blue}]
\def\b{2}
\def\h{2}
\def\p{0.5}
\pgfmathsetmacro{\rx}{\b/2}
\pgfmathsetmacro{\ry}{\rx*\p}
\pgfmathsetmacro{\ta}{90-atan2(\h,\ry)}
\fill[gray!50]
(0, \h) -- (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry) -- cycle;
\fill[gray!75] coordinate (bottom) ellipse [x radius=\rx, y radius=\ry];
\draw[dashed] (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry);
\draw (0, \h) -- (\ta:\rx+0 and \ry) arc (\ta:-180-\ta:\rx+0 and \ry) -- coordinate[pos=.4](hypbend) cycle;
\begin{scope}[rotate around={180:(0,\h)}]
\fill[gray!50]
(0, \h) -- (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry) -- cycle;
\fill[gray!75] coordinate (top) ellipse [x radius=\rx, y radius=\ry];
\draw (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry) (0, \h) -- coordinate[pos=.3](parabend) (\ta:\rx+0 and \ry) arc (\ta:-180-\ta:\rx+0 and \ry) -- cycle;
\end{scope}
%% Dots & Axis
\fill (top) circle[radius=1pt] (0,\h) circle[radius=1pt] (bottom) circle[radius=1pt];
\draw[dotted] (top) -- (bottom);
\draw (top) -- ++(-90:\rx+0 and \ry);
%% Parabola
\path (top) +(50+50*\p:\rx+0 and \ry) coordinate (tmp) +(-50+50*\p:\rx+0 and \ry) coordinate (tmp2);
\draw[parabola] (tmp) ..controls ++(-90:0) and ++(\ta+90:\p).. (parabend) node[left]{Parabola} ..controls ++(\ta-90:\p) and ++(-90:0).. (tmp2);
%% Circle
\def\pos{0.5}
\draw[circle] (0,\pos*\h) ellipse [x radius=\pos*\rx, y radius=\pos*\ry] +(180:\pos*\rx) node[above left]{Circle};
%% Hyperbola
\path (bottom) +(130-50*\p:\rx+0 and \ry) coordinate (tmp) +(230+50*\p:\rx+0 and \ry) coordinate (tmp2);
\draw[hyperbola] (tmp) ..controls ++(90:0) and ++(90-\ta:0.6*\p).. (hypbend) node[left]{Hyperbola} ..controls ++(-\ta-90:0.6*\p) and ++(90:0).. (tmp2);
\end{tikzpicture}
\end{document}

You can play around with the perspective value to get it better adjusted. And please, do take note that I don't claim this drawing to be truthfully when it comes to 3D, this is merely an ilusion of perspective, I did not calculate anything to ensure truthful perception of depth!!

Answer 2

please, I'm making some modifications.For now I need to add the plane that intersects the cones and see that the intersection is the conic sought

\documentclass[12pt,a4paper]{article}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amscd}
\usepackage[latin2]{inputenc}
\usepackage{t1enc}
\usepackage[mathscr]{eucal}
\usepackage{indentfirst}
\usepackage{graphicx}
\usepackage{graphics}
\usepackage{pict2e}
\usepackage{epic}
\numberwithin{equation}{section}
\usepackage{epstopdf} 
\usepackage{pgf,tikz,tkz-euclide}
\usepackage{tikz-3dplot}
\usetikzlibrary{calc,patterns,angles,quotes,arrows,intersections,through,backgrounds,arrows.meta}
\usetkzobj{all}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns}
\title{Conicas : }
\begin{document}
\maketitle
\begin{center}
\begin{tikzpicture}[parabola/.style={very thin, red}, hyperbola/.style={very thin, violet}, circle/.style={very thin, blue}]
\def\b{2}
\def\h{2}
\def\p{0.5}
\pgfmathsetmacro{\rx}{\b/2}
\pgfmathsetmacro{\ry}{\rx*\p}
\pgfmathsetmacro{\ta}{90-atan2(\h,\ry)}

\fill[white](0, \h) -- (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry) -- cycle;
\fill[white] coordinate (bottom) ellipse [x radius=\rx, y radius=\ry];
\draw[dashed] (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry);
\draw (0, \h) -- (\ta:\rx+0 and \ry) arc (\ta:-180-\ta:\rx+0 and \ry) -- coordinate[pos=.4](hypbend) cycle;
\begin{scope}[rotate around={180:(0,\h)}]
\fill[white](0, \h) -- (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry) -- cycle;
\fill[white] coordinate (top) ellipse [x radius=\rx, y radius=\ry];
\draw (\ta:\rx+0 and \ry) arc (\ta:180-\ta:\rx+0 and \ry) (0, \h) -- coordinate[pos=.3](parabend) (\ta:\rx+0 and \ry) arc (\ta:-180-\ta:\rx+0 and \ry) -- cycle;
\end{scope}

%% Parabola
\path (top) +(50+50*\p:\rx+0 and \ry) coordinate (tmp) +(-50+50*\p:\rx+0 and \ry) coordinate (tmp2);
\fill[parabola,gray!50] (tmp) ..controls ++(-90:0) and ++(\ta+90:\p).. (parabend) node[left]{Parabola} ..controls ++(\ta-90:\p) and ++(-90:0).. (tmp2);

%% Dots & Axis
\fill (top) circle[radius=1pt] (0,\h) circle[radius=1pt] (bottom) circle[radius=1pt];
\draw[dotted] (top) -- (bottom);
\draw (top) -- ++(-90:\rx+0 and \ry);
\end{tikzpicture}
\end{center}
\end{document}