hiiiii

 

Let us try to find the point of intersection of the two lines ..

 

SO let us solve 3x-y-43k = 0

                and, 3kx+ky-43 = 0 simlutaneously

 

Solving we get x = 2(k² + 1)/k

 

              and  y = 23(k² - 1)/k 

 

and,        now if we find (x)² - (y/3)² 

 

we get   (x)² - (y/3)²  = 16

 

so, x²/16 - y²/48 = 1  

 

This is equation of hyperbola and the eccentrity is clearly (48/16 + 1) = 2

 

I hope u have got the question ...

 

cheers