JEE Math Practice Question

If tangents are drawn to the ellipse x2 + 2y2 = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :

1. A.$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$
2. B.$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$
3. C.$${1 \over {4{x^2}}} + {1 \over {2{y^2}}} = 1$$
4. D.$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$