With x1 = x2 = 0, arc_length_expr is equal to 0, meaning your eq3 is
invalid. You can see this if you print eq3. It gets set to False,
because it is 0 = 10.

Aaron Meurer

On Sat, May 25, 2024 at 5:26 PM Shishir Kushwaha
<[email protected]> wrote:
>
> In the following piece of code I am  unable to get the values of a,b and c 
> after solving them.
> Is there a different way to solve it and what am i doing wrong. Take x1 = 0 , 
> y1=10, x2=0, y2=10, length = 20.
>
> def get_lowest_point(self):
> a, b, c, x = symbols('a b c x')
>
> x1, y1 = self._left_support
> x2, y2 = self._right_support
> length = self._length
>
> eq1 = Eq(a * x1**2 + b * x1 + c, y1)
> eq2 = Eq(a * x2**2 + b * x2 + c, y2)
> arc_length_expr = integrate(sqrt(1 + (2 * a * x + b)**2),
> (x, x1, x2))
> eq3 = Eq(arc_length_expr, length)
> solution = solve((eq1, eq2, eq3), (a, b, c))
>
> # Print the solution to debug
> print("Solution:", solution)
>
> return solution
>
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