Question: how to find ideal from parametric equations

1. if parametric equations are
x0 = a^4, x1=a^3*b, x2=a^2*b^2, x3=a*b^3, x4=b^4

how to find ideal below

e12 = x0*x2-x1^2
e13 = x0*x3-x1*x2
e14 = x0*x4-x1*x3
e23 = x1*x3-x2^2
e24 = x1*x4-x2*x3
e34 = x2*x4-x3^2

2.
if let y_i = x_i/x0 for i = 1..4
how to find above parametrically by below equations
y1 = b
y2 = b^2
y3 = b^3
y4 = b^4

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