The tangents to the hyperbola are parallel to the straight line at the following points
(2, 1) or (1, 2)
(2, −1) or (−2, 1)
(−1, −2)
(−2, −1)
Clearly tangents at (2, –1) or (–2, 1) are parallel to 2x + y + 8 = 0.
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