Plot hyperbola

I want to graph an equation $x^2 - 9y^2 +2x + 36y - 44 = 0$

In [1]:

#packages
import numpy as np
from sympy import *
from sympy.plotting import plot, plot_implicit, plot_parametric

In [2]:

x, y = symbols('x y')
plot_implicit(Eq(x**2-9*y**2+2*x+36*y-44, 0), (x,-10,10))

<sympy.plotting.plot.Plot at 0x7f8f8c8872b0>

The graph below is for the equation $\frac{x^2}{9} - \frac{y^2}{1} = 1.$ It is an east-west hyperbola.

In [3]:

plot_implicit(Eq(x**2/9- y**2, 1), (x,-10,10))

<sympy.plotting.plot.Plot at 0x7f8f8e3d55f8>

The graph below is for the equation $\frac{x^2}{1} - \frac{y^2}{9} = 1.$ It is still east-western hyperbola

In [4]:

plot_implicit(Eq(x**2- y**2/9, 1), (x,-5,5))

<sympy.plotting.plot.Plot at 0x7f8f8a3e17b8>

The graph below is for the equation $- \frac{x^2}{9} + \frac{y^2}{1} = 1.$ Compared to the above equations, we switch the sign of $x$ term and $y$ term. Now, it becomes south-north hyperbola.

In [5]:

plot_implicit(Eq(-x**2/9 + y**2, 1), (x,-10,10))

<sympy.plotting.plot.Plot at 0x7f8f8a31dd30>

I want to plot $25 x^2 + 50 x + 169 y^2 - 676 y = 3524$

In [17]:

x, y = symbols('x y')
p1 = plot_implicit(Eq(25*x**2 + 50* x + 169 * y**2 - 676 * y - 3524, 0), (x, -15, 15));
#p1.save('fig1.png')

In [0]: