Orbit Collision: Find New Earth Orbit Axes (A,B) in Terms of R

[me9900]

Homework Statement

If Halley's comet hits the Earth head on and after the collision the Earth continues to move in its initial direction but with 12% greater speed, find the new semi-major and semi-minor axes on the new Earth orbit in terms of the earth-sun distance (R) for the present circular orbit of the earth.

Homework Equations

F=ma
F=GMm/r^2

The Attempt at a Solution

 

[HalfThere]

Remember that the Earth's angular momentum is conserved through its orbit.
L = mvr

And consider that, since the Earth's new velocity is in the same direction as before, it would go back to R for its semi-minor axis, due to the fact that the new velocity is in a single coordinate only, and it therefore has no force pushing it tangentially from its original path - it only moves tangential relative to it's old path as it diverges from it due to higher speed.

 

[me9900]

I don't necessarily agree with R remaining as the semi-minor axis because the origin of orbit(now an ellipse) isn't at the previous focus (being the sun). However, could R be given by a-c=R or (semi-major axis)-(distance from origin to focus)=R ?