Finding Conic Equation Using Distance Formula Help Needed!

Hey there. I'm a sophomore in high school and I could definitely use some hel. I have been going at a couple problems my teacher gave me for numerous hours, but I just don't think I am doing it right. Here is what I am supposed to do:

Start with the formal distance definition and then find the standard form of the conics described in each problem:

The set of all points in a plane such the sum of the distances from the points (4,11) and (4,-5) is 34.

Another problem that I am having trouble with:

The set of all points in a plane such the difference of the distances from the points (-8,3) and (18,3) is 10.

Any help on these problems would be much appreciated and I have given it my best on my own, but that doesn't seem to have worked so I do need some help. Thanks.