Given: A hyperbola is formed by the locus of the point of intersection of lines

To find: Eccentricity of the hyperbola

Multiply by λ:

Adding (1) and (2):

Now, From (1):

Squaring both sides:

From (3) and (4):

Formula used:

For hyperbola

Eccentricity(e) is given by,

⇒ c = 8

Therefore,

⇒ e = 2

Hence, eccentricity of hyperbola is 2