Roots of a Polynomial in a PolynomialRing

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If I do:

R.<x,y>= PolynomialRing(QQ,2)

f=x^2-y^2

f.roots()

Why it doesn't work? And next code work:

R.<x>= PolynomialRing(QQ)

f=x^2-1

f.roots()

I don't understand why.

And one more things, If I want to define all polinomials as this form -> ax^2 - by^2 where $a$ and $b$ are constants. Have I do this?

R.<a,b,x,y>=PolynomialRing(QQ,4)

I=R.Ideal([a*x^2 - b*y^2])

f= 2*x^2 - 3*y^2

How can I do that?

Thank you so much.