JEE Math Practice Question

The locus of the point of intersection of the lines, $$\sqrt 2 x - y + 4\sqrt 2 k = 0$$ and $$\sqrt 2 k\,x + k\,y - 4\sqrt 2 = 0$$ (k is any non-zero real parameter), is :

1. A.an ellipse whose eccentricity is $${1 \over {\sqrt 3 }}.$$
2. B.an ellipse with length of its major axis $$8\sqrt 2 .$$
3. C.a hyperbola whose eccentricity is $$\sqrt 3 .$$
4. D.a hyperbola with length of its transverse axis $$8\sqrt 2 .$$