Write a program where you can enter an ellipse equation and a straight line equation (each in coordinate form).

If nothing is entered, use the values 16*x**2 + 9*y**2 = 144 and -x + y = 5. With the help of sympy.sympify you can convert the input into a SymPy expression and then use SymPy to calculate the intersection points of the straight line and ellipse.

Now indicate whether the straight line entered is a secant, a tangent or a passersby of the ellipse entered.

Plot both using sympy.plotting.plotimplicit or use matplotlib if you prefer. However, the straight line and the ellipse should be plotted together.