If necessary, you can solve for the places on the line:
If x = 1:
1 / x - 1 / y = 4.
1 / 1 - 1 / y = 4.
1 - 1 / y = 4.
- 1 / y = 3.
- y = 1 / 3.
y = -1 / 3.
At q(1, -1 / 3) both methods are equal:
y² / x² = (-1 / 3)² / 1² = 1 / 9.
(1 + 4y) / (1 - 4x) = (1 + 4 * (-1 / 3)) / (1 - 4 * 1) = (-1 / 3) / -3 = 1 / 9.
Or, if y = 2:
1 / x - 1 / y = 4.
1 / x - 1 / 2 = 4.
1 / x = 9 / 2.
x = 2 / 9.
At r(2 / 9, 2), both methods are equal:
y² / x² = 2² / (2 / 9)² = 4 / (4 / 81) = 81.
(1 + 4y) / (1 - 4x) = (1 + 4 * 2) / (1 - 4 * (2 / 9)) = 9 / (1 / 9) = 81.