If 2 x - y + 1 = 0 is a tangent to the hyperbola x 2 a 2 - y 2 16 = 1 , then which of the following CANNOT be sides of a right angled triangle?

Step-by-step solution

The line y = m x + c is tangent to hyperbola x 2 a 2 - y 2 b 2 = 1 , , if c 2 = a 2 m 2 - b 2 ∴ 1 2 = 4 a 2 - 16 ⇒ a 2 = 17 4 ⇒ a = 17 2 For 2 a , 4, 1 , sides are 17 , 4 , 1 ( ⇒ Right angled triangle) For 2a, 8, 1 , sides are 17 , 8 , 1 ( ⇒ Triangle is not possible) For a, 4, 1 , sides are 17 2 , 4 , 1 ( ⇒ Triangle is not possible) For a, 4, 2 , sides are 17 2 , 4 , 2 ( ⇒ Triangle exist but not right angled)