Let q1, q2 be the generalized coordinates and p1, p2 be the conjugate momenta, respectively. Let a and b be such that
Q1 = q1, P1 = ap1 + 16 p2
Q2 = p2, P2 = 2q1 + b q2
is a canonical transformation. Then which of the following statements are true?
1
a2 + b2 = 2
2
a - b = 2
3
a + b = 2
4
a = 1, b = 1