Planet orbiting around a star whose mass changes

It helps, but you need another equation. What else will be conserved?
(But I have a concern about the question. It seems to assume the new orbit will be circular. That strikes me as most unlikely.)

 

Looks ok. The trouble with questions with premisses that defy physical laws is that there may well be different solutions methods, all valid, that produce different answers.

Edit: and gneill has put his finger on just such an alternate answer. As I asked in post #2, what else should be conserved?

 

As I read the problem and guess at the author's thoughts, we are to assume that at the same moment half of the star magically vanishes, the planet does not change mass, but magically teleports to a new position with a new velocity, which are both chosen so that angular momentum is conserved and a circular orbit results.

It is strange that one would pose a problem in which angular momentum conservation is paramount using a scenario involving teleportation. Teleportation defies conservation of angular momentum.

Of course, neither linear nor angular momentum are conserved in this problem anyway. The star changes mass. That defies conservation of both quantities in a great number of frames of reference.

 

As gneill and I have hinted, the author probably did not mean to imply assumption of a new circular orbit; rather, that something else is conserved.
Those two alternate assumptions lead to different answers.