Solve a Quadratic Equation in two variables using Python

I have got two equations, one linear say,

, where m and c are constants and the other quadratic say,

, where x1, y1 and r are constants.

Is there a way I can solve for x and y using Python ?

I could solve them on pen and paper finding the relation between x and y from the linear equation and substituting it in the other. There would be two roots satisfying the quadratic equation.

Look at SymPy.

Here is an example of how to solve a simple difference of squares equation, taken from their documentation.

>>> from sympy.solvers import solve
>>> from sympy import Symbol

>>> x = Symbol('x')
>>> solve(x**2 - 1, x)

[-1, 1]

Regarding your specific problem, the solution will look something like this:

>>> x = Symbol('x')
>>> y = Symbol('y')

>>> solve( (x-c1)**2 + (y-c2)**2 - c3**2, x, y)

c1, c2 and c3 are the constants declared as variables earlier in your code.