checkpoint saved.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Conic section Graphs\n",
      "Menu \n",
      " 1. Parabola \n",
      " 2. Ellipse and circles \n",
      " 3. Hyperbolas \n",
      " 4.EXIT\n",
      " Please enter any one of the options  3\n",
      "HYPERBOLA\n",
      "*** PRO TIP : Users are requested to use values less than 50, for best results :) ***\n",
      "MENU \n",
      " 1. Hyperbola in standard equation \n",
      " 2. Hyperbola in Expanded equation \n",
      " 3.EXIT\n",
      "Choose an option34\n",
      "HYPERBOLA\n",
      "*** PRO TIP : Users are requested to use values less than 50, for best results :) ***\n",
      "MENU \n",
      " 1. Hyperbola in standard equation \n",
      " 2. Hyperbola in Expanded equation \n",
      " 3.EXIT\n",
      "Choose an option1\n",
      "1. Hyperbolas in standard equation are of the form\n",
      "x^2/A^2 - y^2/B^2 = 1 \n",
      " Please enter the Value of A 43\n",
      " Please enter the Value of B 56\n",
      "Do you Want to see directrix and focus as well ? \n",
      "  y for YES and n for NO y\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HYPERBOLA\n",
      "*** PRO TIP : Users are requested to use values less than 50, for best results :) ***\n",
      "MENU \n",
      " 1. Hyperbola in standard equation \n",
      " 2. Hyperbola in Expanded equation \n",
      " 3.EXIT\n",
      "Choose an option3\n",
      "Conic section Graphs\n",
      "Menu \n",
      " 1. Parabola \n",
      " 2. Ellipse and circles \n",
      " 3. Hyperbolas \n",
      " 4.EXIT\n",
      " Please enter any one of the options  2\n",
      "ELLIPSE AND CIRCLES\n",
      "MENU \n",
      " 1. Circle  \n",
      " 2. Ellipse in Standard equation \n",
      " 3. Ellipse in Expanded equation \n",
      " 4.EXIT\n",
      "Choose an option2\n",
      "2. Ellipse in Standard equation\n",
      "x^2/A^2 + y^2/B^2 = 1\n",
      " Please enter the Value of A 6\n",
      " Please enter the Value of B 9\n",
      "Do you Want to see directrix and focus as well ? \n",
      "  y for YES and n for NO n\n",
      "Please enter x coordinate of centre   67\n",
      "Please enter y coordinate of centre   65\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ELLIPSE AND CIRCLES\n",
      "MENU \n",
      " 1. Circle  \n",
      " 2. Ellipse in Standard equation \n",
      " 3. Ellipse in Expanded equation \n",
      " 4.EXIT\n",
      "Choose an option4\n",
      "Conic section Graphs\n",
      "Menu \n",
      " 1. Parabola \n",
      " 2. Ellipse and circles \n",
      " 3. Hyperbolas \n",
      " 4.EXIT\n",
      " Please enter any one of the options  4\n",
      "EOP\n"
     ]
    }
   ],
   "source": [
    "#Importing all the required Libraries\n",
    "\n",
    "#Importing matplotlib\n",
    "import matplotlib.pyplot as mpl\n",
    "\n",
    "#Impoting numpy\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "#Defining values for x and y\n",
    "x = np.linspace(-50, 51, 200)\n",
    "y = np.linspace(-50, 51, 200)\n",
    "#meshgrid makes an array, this is useful in defining functions\n",
    "x, y = np.meshgrid(x, y)\n",
    "\n",
    "#Axes() as a function, this will highlight our origin\n",
    "def axes():\n",
    "    mpl.axhline(0, alpha= .2, linewidth= 2, color='k' )\n",
    "    #Printing Horizontal line, X axis\n",
    "    mpl.axvline(0, alpha= .2, linewidth= 2, color='k' )\n",
    "    #Printing Vertical line, Y axis\n",
    "    #mpl.axis('equal')\n",
    "\n",
    "#For taking valid inputs as values, defining a f(n)\n",
    "def options(prompt):\n",
    "    while True:\n",
    "        try:\n",
    "            #Ensuring the input to be integer\n",
    "            number = int(input(prompt))\n",
    "            break\n",
    "        except ValueError :\n",
    "            #Printing Output for correction, Giving user another chance to enter value\n",
    "            print('Please enter a Valid input ')\n",
    "            pass\n",
    "    return number\n",
    "def delta(a,b,c,f,g,h):\n",
    "    if a*(b)*c +2*f*g*h -a*f^2 -b*g^2 -c*h^2 != 0:\n",
    "        return True\n",
    "    else :\n",
    "        return False\n",
    "   \n",
    "\n",
    "while True :\n",
    "    print('Conic section Graphs')\n",
    "    print('Menu \\n 1. Parabola \\n 2. Ellipse and circles \\n 3. Hyperbolas \\n 4.EXIT')\n",
    "    opts = options(' Please enter any one of the options  ')\n",
    "    if opts == 1:\n",
    "        while True:\n",
    "            print('PARABOLA')\n",
    "            print(\"MENU \\n 1. Parabola in standard equation \\n 2. Parabola in Expanded equation \\n 3.EXIT\")\n",
    "            ch = int(input('Choose an option'))\n",
    "            if ch == 1:\n",
    "                print('1. Parabola in standard equation')\n",
    "                a = float(input('Please enter the value of \\'a\\' '  ))\n",
    "                print(' Parabolas in standard eqn are of the form \\n y^2 = 4ax ')\n",
    "                print('Do you Want to see directrix and focus as well ? ')\n",
    "                duff = input ('  y for YES and n for NO ')\n",
    "                if duff == 'y':\n",
    "                    axes()\n",
    "                    # Printing Focus as a DOT.\n",
    "                    mpl.plot(a, 0, '.')\n",
    "                    # Printing Directrix, using a vertical line axvline.\n",
    "                    mpl.axvline(-a)\n",
    "                    mpl.contour(x, y, (y**2 - 4*a*x), [0], colors='r' )\n",
    "                    mpl.show()\n",
    "                   \n",
    "                else :\n",
    "                    axes()\n",
    "                    mpl.contour(x, y, (y**2 - 4*a*x), [0], colors='k')\n",
    "                    mpl.show()\n",
    "                   \n",
    "            elif ch == 2:\n",
    "                while True:\n",
    "                    print('2. Parabola in Expanded equation')\n",
    "                    print('Parabolas in non-standard eqn are of the form :')\n",
    "                    print('Ax^2+2Hxy+By^2+2Gx+2Fy+C=0, \\n where H^2−4AB=0')\n",
    "                    a = options(' Please enter the Value of A ')\n",
    "                    b = options(' Please enter the Value of B ')\n",
    "                    c = options(' Please enter the Value of C ')\n",
    "                    f = options(' Please enter the Value of F ')\n",
    "                    g = options(' Please enter the Value of G ')\n",
    "                    h = options(' Please enter the Value of H ')\n",
    "                   \n",
    "                   \n",
    "                   \n",
    "                    if delta(a,b,c,f,g,h) and h**2 - 4*a*b == 0 :\n",
    "                        print('Your Equation is : ')\n",
    "                        print('\\t',a,'^2x + ',h*2,'xy + ',b,'y^2 + ',g*2,'x + ',f,'y + ',g,' = 0 ' )\n",
    "                        axes()\n",
    "                        mpl.contour(x, y,(a*x**2 + 2*h*x*y + b*y**2 + 2*g*x + 2*f*y + c), [0], colors='k')\n",
    "                        mpl.show()\n",
    "                    else:\n",
    "                        print('Condition : h**2 - 4*a*b = 0 \\t NOT SATISFIED \\n Try again :( ')\n",
    "                        continue\n",
    "            elif ch == 3 :\n",
    "                 \n",
    "                break\n",
    "            else:\n",
    "                continue\n",
    "    elif opts == 2:\n",
    "        while True:\n",
    "            print('ELLIPSE AND CIRCLES')\n",
    "            print(\"MENU \\n 1. Circle  \\n 2. Ellipse in Standard equation \\n 3. Ellipse in Expanded equation \\n 4.EXIT\")\n",
    "            ch = int(input('Choose an option'))\n",
    "            if ch ==1 :\n",
    "                print('1. Circle')\n",
    "                r= int(input('Please enter radius of circle   '))\n",
    "                h = int(input('Please enter x coordinate of centre   '))\n",
    "                k = int(input('Please enter y coordinate of centre   '))\n",
    "                print('Radius of circle  ',r, 'with centre ','(',h,',',k,')')\n",
    "                t = np.linspace(0,2*np.pi, 1000)\n",
    "                x = r*np.cos(t) + h\n",
    "                y = r*np.sin(t) + k\n",
    "\n",
    "                mpl.axis('equal')\n",
    "                mpl.grid()\n",
    "                mpl.plot(x,y)\n",
    "                mpl.show()\n",
    "            if ch==2:\n",
    "                print('2. Ellipse in Standard equation')\n",
    "                print('x^2/A^2 + y^2/B^2 = 1')\n",
    "                a = options(' Please enter the Value of A ')\n",
    "                b = options(' Please enter the Value of B ')\n",
    "                print('Do you Want to see directrix and focus as well ? ')\n",
    "                duff = input ('  y for YES and n for NO ')\n",
    "                while True:\n",
    "                    if duff == 'y':\n",
    "                        axes()\n",
    "                        h = int(input('Please enter x coordinate of centre   '))\n",
    "                        k = int(input('Please enter y coordinate of centre   '))\n",
    "                        t = np.linspace(0,2*np.pi, 1000)\n",
    "                        p = h + a*np.cos(t)\n",
    "                        q = k + b*np.sin(t)\n",
    "                        mpl.axis('equal')\n",
    "                        mpl.grid()\n",
    "                        mpl.plot(p,q)\n",
    "                        # Defining Eccentricity.\n",
    "                        e = np.sqrt(1 - b**2/a**2)\n",
    "                        # Printing Foci as DOTs.\n",
    "                        mpl.plot(a*e, 0, '.', -a*e, 0, '.')\n",
    "                        # Printing Directrix, using a vertical lines axvline\n",
    "                        mpl.axvline(a/e)\n",
    "                        mpl.axvline(-a/e)\n",
    "                        mpl.show()\n",
    "                        break\n",
    "                    elif duff == 'n' :\n",
    "                        axes()\n",
    "                        h = int(input('Please enter x coordinate of centre   '))\n",
    "                        k = int(input('Please enter y coordinate of centre   '))\n",
    "                        t = np.linspace(0,2*np.pi, 1000)\n",
    "                        p = h + a*np.cos(t)\n",
    "                        q = k + b*np.sin(t)\n",
    "                        mpl.axis('equal')\n",
    "                        mpl.grid()\n",
    "                        mpl.plot(p,q)\n",
    "                        mpl.show()\n",
    "                        break\n",
    "                    else :\n",
    "                        continue\n",
    "\n",
    "            if ch ==3:\n",
    "                while True:\n",
    "                    print('3. Ellipse in Expanded equation')\n",
    "                    print('For ellipses, the eccentricity,e is 0<e<1 \\n It is defined as e**2 = 1 - B**2/A**2 ')\n",
    "                    print('To define a ellipse in a non-standard position is has to follow the form :')\n",
    "                    print('Ax^2+2Hxy+By^2+2Gx+2Fy+C=0, \\n where H^2−4AB<0')\n",
    "                    a = options(' Please enter the Value of A ')\n",
    "                    b = options(' Please enter the Value of B ')\n",
    "                    c = options(' Please enter the Value of C ')\n",
    "                    f = options(' Please enter the Value of F ')\n",
    "                    g = options(' Please enter the Value of G ')\n",
    "                    h = options(' Please enter the Value of H ')\n",
    "                    if delta(a,b,c,f,g,h) and h**2 - 4*a*b < 0:\n",
    "                        print('Your Equation is : ')\n",
    "                        print('\\t',a,'^2x + ',h*2,'xy + ',b,'y^2 + ',g*2,'x + ',f,'y + ',g,' = 0 ' )\n",
    "         \n",
    "                        axes()\n",
    "                        mpl.contour(x, y,(a*x**2 + 2*h*x*y + b*y**2 + 2*g*x + 2*f*y + c), [0], colors='k')\n",
    "                        mpl.show()\n",
    "                        break\n",
    "                    else :\n",
    "                        print('Condition : h**2 - 4*a*b < 0 \\t NOT SATISFIED \\n Try again :( ')\n",
    "                        continue\n",
    "   \n",
    "            elif ch==4:\n",
    "                break\n",
    "            else:\n",
    "                continue\n",
    "    elif opts == 3:\n",
    "        q = np.linspace(-100, 101, 200)\n",
    "        w = np.linspace(-100, 101, 200)\n",
    "        q, w = np.meshgrid(q, w)\n",
    "        while True:\n",
    "            print('HYPERBOLA')\n",
    "            print('*** PRO TIP : Users are requested to use values less than 50, for best results :) ***')\n",
    "            print(\"MENU \\n 1. Hyperbola in standard equation \\n 2. Hyperbola in Expanded equation \\n 3.EXIT\")\n",
    "            ch = int(input('Choose an option'))\n",
    "            if ch == 1:\n",
    "                print('1. Hyperbolas in standard equation are of the form')\n",
    "                print('x^2/A^2 - y^2/B^2 = 1 ')\n",
    "                a = options(' Please enter the Value of A ')\n",
    "                b = options(' Please enter the Value of B ')\n",
    "       \n",
    "                print('Do you Want to see directrix and focus as well ? ')\n",
    "                duff = input ('  y for YES and n for NO ')\n",
    "                while True:\n",
    "                    if duff == 'y':\n",
    "           \n",
    "                        axes()\n",
    "                        mpl.contour(q, w,(q**2/a**2 - w**2/b**2), [1], colors='k')\n",
    "                        # Defining Eccentricity.\n",
    "                        e = np.sqrt(1 + b**2/a**2)\n",
    "                        # Printing Foci as DOTs.\n",
    "                        mpl.plot(a*e, 0, '.', -a*e, 0, '.')\n",
    "                        # Printing Directrix, using a vertical line axvline\n",
    "                        mpl.axvline(a/e)\n",
    "                        mpl.axvline(-a/e)\n",
    "                        mpl.show()\n",
    "                        break\n",
    "                    elif duff =='n' :\n",
    "                        axes()\n",
    "                        mpl.contour(q, w,(q**2/a**2 - w**2/b**2), [1], colors='k')\n",
    "                        mpl.show()\n",
    "                        break\n",
    "                    else:\n",
    "                        continue\n",
    "            elif ch == 2:\n",
    "                while True:\n",
    "                    print('2. Hperbola in Expanded equation')\n",
    "                    print('Hyperbolas in non-standard eqn are of the form ::')\n",
    "                    print('Ax^2+2Hxy+By^2+2Gx+2Fy+C=0, \\n where H^2−4AB=0')\n",
    "                    a = options(' Please enter the Value of A ')\n",
    "                    b = options(' Please enter the Value of B ')\n",
    "                    c = options(' Please enter the Value of C ')\n",
    "                    f = options(' Please enter the Value of F ')\n",
    "                    g = options(' Please enter the Value of G ')\n",
    "                    h = options(' Please enter the Value of H ')\n",
    "       \n",
    "                    if delta(a,b,c,f,g,h) and h**2 - 4*a*b > 0 :\n",
    "                        print('Your Equation is : ')\n",
    "                        print('\\t',a,'^2x + ',h*2,'xy + ',b,'y^2 + ',g*2,'x + ',f*2,'y + ',c,' = 0 ' )\n",
    "                        axes()\n",
    "                        mpl.contour(x, y,(a*x**2 + b*x*y + c*y**2 + d*x + e*y + f), [0], colors='k')\n",
    "                        mpl.show()\n",
    "                        break\n",
    "                    else:\n",
    "                        print('Condition : h**2 - 4*a*b > 0  \\t NOT SATISFIED \\n Try again :( ')\n",
    "                        continue\n",
    "            elif ch == 3 :\n",
    "                break\n",
    "            else:\n",
    "                continue\n",
    "    if opts == 4:\n",
    "        break\n",
    "print('EOP')"
   ]
  },
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