Solution: Find the equation of the circle with centre (3,-2) and radius 5.

Code:

import sympy

h, k = 3, -2
r = 5
x, y = sympy.symbols('x y')

# Standard form: (x - h)^2 + (y - k)^2 = r^2
lhs = (x - h)**2 + (y - k)**2
rhs = r**2

# Expanded form
expanded_eq = sympy.expand(lhs - rhs)

print(f"h={h}, k={k}, r={r}")
print(f"Standard form: (x - {h})^2 + (y - ({k}))^2 = {r}^2")
print(f"Expanded form: {expanded_eq} = 0")

Output:

h=3, k=-2, r=5
Standard form: (x - 3)^2 + (y - (-2))^2 = 5^2
Expanded form: x**2 - 6*x + y**2 + 4*y - 12 = 0