Given that we need to find the length of the intercept made by the circle x² + y² + 2x - 4y - 5 = 0 on the y - axis.

For finding the length of intercept we first need to find the intercept made by the circle with the y - axis.

We know that on the y - axis, the value of x is 0.

By substituting x = 0 in the circle equation we get,

⇒ 0² + y² + 2(0) - 4y - 5 = 0

⇒ y² - 4y - 5 = 0

⇒ y² - 5y + y - 5 = 0

⇒ y(y - 5) + 1(y - 5) = 0

⇒ (y + 1)(y - 5) = 0

⇒ y + 1 = 0 or y - 5 = 0

⇒ y = - 1 or y = 5.

The points intersected by the circle are A(- 1,0) and B(5,0).

We know the length of the intercept is AB.

⇒

⇒

⇒ AB = 6.

∴The length of the intercept is 6.