Hmm! I am sorry but from that small pic it is impossible to say what the tree might be.
Conifers are hard to id at the best of times, even standing infront of them or with excellent close up pics showing good detail.
I am left with many questions. For example how close to your house is this tree?
How tall is it?
This may help you. It gives an idea of how far roots grow.
Is this conifer on the boundary of your property?
Does it overhang your land?
If so you can legal cut back any /all branches that overhang your boundary. (Provided you offer all the cut branches back to the owner of the tree.If they do not want them then please do not dump them on their side, but dispose of them as your local authority would wish.)
Do not cut a fraction over the boundary, that is illegal. You could be taken to court.
Tall conifers especially the dreaded Leylandii cause enormous problems / disputes between neighbours.
People have even been murdered after disputes about conifer hedges.. loss of light etc.
My advise would be to pop round and have a quiet amicable chat.
Say you are very concerned about the roots affecting your home. Tell them you are losing light.
May be they will be willing to take the top out.( which could ruin the shape)
Maybe they might agree to cut it down.
Failing that then you may be left with nothing you can do about it.
If it were a hedge of Leylandii there are now laws to protect neighbours. However, as far as I am aware this does not apply to a single specimen conifer.
See also ...