What are the points of contact when the line x -y equals 2 crosses the curve x squared -4y squared equals 5 showing work?

Answer 1

If: x -y = 2 then x^2 = (2+y)^2 => 4+4y+y^2

If: x^2 -4y^2 = 5 then x^2 = 5+4y^2

So: 5+4y^2 = 4+4y+y^2

Transposing terms: 3y^2 -4y +1 = 0

Factorizing the above: (3y-1)(y-1) = 0 meaning y = 1/3 or y = 1

By substitution contacts are made at: (7/3, 1/3) and (3, 1)