Pasted

box% sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.2, Release Date: 2020-10-24                     │
│ Using Python 3.8.6. Type "help()" for help.                        │
└────────────────────────────────────────────────────────────────────┘
sage: R.<x1,y1,a,length> = PolynomialRing(QQ, order='lex')
sage: (x0,y0) = (0,0)
sage: (x2,y2) = (x1,-y1)
sage: Q = lambda u, v: (u[0]-v[0])^2 + (u[1]-v[1])^2
sage: ideal(y1^2-4*a*x1, length^2 - Q((x0,y0),(x1,y1)), length^2 - Q((x1,y1),(x2,y2))).groebner_basis()
[x1^2 - 3/4*length^2, x1*a - 1/16*length^2, x1*length^2 - 12*a*length^2, y1^2 - 1/4*length^2, a^2*length^2 - 1/192*length^4]
sage: