Given: A straight line x – 3y = 1 intercepts hyperbola x² – 4y² = 1

To find: Length of the intercepted line

Formula used:

Distance between two points (m, n) and (a, b) is given by

Firstly we will find point of intersections of given line and hyperbola

x – 3y = 1 ⇒ x = 1 + 3y

x² – 4y² = 1

⇒ (1 + 3y)² – 4y² = 1

⇒ 1 + 9y² + 6y – 4y² = 1

⇒ 5y² + 6y = 0

⇒ y(5y + 6) = 0

⇒ y = 0 or 5y + 6 = 0

Now, x = 1 + 3y

So, Point of intersections are A(1, 0) and

Distance between point of intersections is