{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 565
        },
        "id": "LXlSRBeHtETj",
        "outputId": "588cbf01-d670-4e9d-9117-51ac715bebd1"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Ejercicio Extra 3.1.7.\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Parámetros de la hipérbola\n",
        "a = 50  # mm\n",
        "b = 30  # mm\n",
        "\n",
        "# Generar valores de t\n",
        "t = np.linspace(-2, 2, 400)  # Ajustar rango para visualizar correctamente\n",
        "\n",
        "# Coordenadas de la hipérbola\n",
        "x = a * np.cosh(t)\n",
        "y = b * np.sinh(t)\n",
        "\n",
        "# Dibujar la hipérbola (rama derecha)\n",
        "plt.figure(figsize=(6,6))\n",
        "plt.plot(x, y, 'b', label='Hipérbola rama derecha')\n",
        "plt.plot(x, -y, 'b', label='Hipérbola rama izquierda')\n",
        "\n",
        "# Dibujar asíntotas\n",
        "x_asint = np.linspace(-a*5, a*5, 500)\n",
        "y_asint_pos = (b/a) * x_asint\n",
        "y_asint_neg = -(b/a) * x_asint\n",
        "plt.plot(x_asint, y_asint_pos, 'r--', label='Asíntota positiva')\n",
        "plt.plot(x_asint, y_asint_neg, 'r--', label='Asíntota negativa')\n",
        "\n",
        "# Configuración del gráfico\n",
        "plt.title(f\"Hipérbola x^2/{a**2} - y^2/{b**2} = 1 con asíntotas\")\n",
        "plt.xlabel(\"X (mm)\")\n",
        "plt.ylabel(\"Y (mm)\")\n",
        "plt.grid(True)\n",
        "plt.axhline(0, color='gray', linestyle='--')\n",
        "plt.axvline(0, color='gray', linestyle='--')\n",
        "plt.axis('equal')\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    }
  ]
}