hyperbola.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyperbola"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "xmin, xmax= -6, 6\n",
    "\n",
    "x = np.linspace(xmin-0.0002, xmax+0.0000017, 1000)\n",
    "\n",
    "tol = 12\n",
    "ymin, ymax = -tol, tol\n",
    "\n",
    "# plt.axvline(x=0, ymin=ymin, ymax=ymax, lw=1, color='k')\n",
    "# plt.axhline(y=0, xmin=xmin, xmax=xmax, lw=1, color='k')\n",
    "\n",
    "xticks = np.arange(int(xmin), int(xmax)+1)\n",
    "yticks = np.arange(int(ymin), int(ymax)+1)\n",
    "\n",
    "\n",
    "y = []\n",
    "y.append((1/x, \"$y=\\\\frac{1}{x}$\"))\n",
    "y.append((2/x, \"$y=\\\\frac{2}{x}$\"))\n",
    "y.append((2/(x) - 4, \"$y=\\\\frac{2}{x} - 4$\"))\n",
    "y.append((np.abs(2/(x) - 4), \"$y=\\|\\\\frac{2}{x} - 4\\|$\"))\n",
    "\n",
    "\n",
    "for _y in y:\n",
    "    t = _y[0]\n",
    "    t[(t<-tol) + (t> tol)] = np.nan\n",
    "\n",
    "for i in range(len(y)-1):\n",
    "\n",
    "    fig = plt.figure()\n",
    "    ax = fig.gca()\n",
    "\n",
    "    for xt in xticks:\n",
    "        ax.axvline(x=xt, ymin=ymin, ymax=ymax, lw=1, ls='-.' if xt != 0 else '-', color='k'  if xt == 0 else 'lightgrey')\n",
    "\n",
    "    for yt in yticks:\n",
    "        ax.axhline(y=yt, lw=1, ls='-.' if yt != 0 else '-', color='k' if yt == 0 else 'lightgrey')\n",
    "\n",
    "    ax.set_xticks(ticks=xticks)\n",
    "    ax.set_yticks(ticks=yticks)\n",
    "\n",
    "    plt.ylim(-8,8)\n",
    "\n",
    "    ax.plot(x, y[i][0], label=y[i][1])\n",
    "    ax.plot(x, y[i+1][0], label=y[i+1][1])\n",
    "    # plt.plot(x, y[i+1][0], label=y[i+1][1])\n",
    "    ax.legend()\n",
    "    plt.draw()\n",
    "    \n",
    "    plt.savefig(f'pics/hyperbola_{i}.png')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y=x^2$\n",
    "\n",
    "$y = -x$\n",
    "\n",
    "$y = x^2 - x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}