The equation of a tangent to the hyperbola, 4 x 2 - 5 y 2 = 20 , parallel to the line x - y = 2 , is

Step-by-step solution

The slope of a line a x + b y + c = 0 is m = - a b . Thus, the slope of the line x - y = 2 is m = - 1 - 1 = 1 and we know that if two lines are parallel then their slopes are equal, hence the slope of the tangent is also m = 1 . The given hyperbola is x 2 5 - y 2 4 = 1 The equation of the tangent to the hyperbola x 2 a 2 - y 2 b 2 = 1 having slope m is y = m x ± a 2 m 2 - b 2 . Hence, the equation of its tangent having slope 1 is y = x ± 5 × 1 2 - 4 ⇒ y = x ± 1 Thus, the tangents are x - y