Cartesian Curve Plot/Lemniscate.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2777cef2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import plot_implicit, symbols, Eq\n",
    "x,y = symbols('x y')\n",
    "p1 = plot_implicit(Eq(2**2*y**2,x**2*(2**2-x**2)),(x,-5,5),(y,-5,5),title='lemniscate: a^2*y^2 = x^2(a^2-x^2),a=2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "67d74ace",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}