Tangents are drawn to the hyperbola x²/9 - y²/4 = 1, parallel to the straight line 2x - y = 1. The points of contact of the tangents on the hyperbola are (9√2, 1√2), (-9√2, -√2), (3√3, -2√2), (-3√3, 2√2)

Let the point of contact of tangents on the hyperbola have coordinates (x1, y1). So, the equation of a tangent is xx1/9 - yy1/4 = 1 (1)The slope of the required tangent to the hyperbola is 2. For y = mx + c to be a tangent to the hyperbola c² = a²m² - b² ⇒ c = ±√9 × 4 = ±√36 = ±6Hence, equations of the tangents are y = 2x ± 6 ⇒ 2x - y = ±6 (2)Equating (1) and (2) we get x1/(2 × 9) = y1/(4 × 1) = 1/±6 ⇒ x1 = ±9√2, y1 = ±√2B is correct.