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.

Is it supposed to be d1+d2=10 for the first one where d1 is sq root[(x-4)^2+(y-11)^2]+ sq.root[(x-4)^2+(y+5)^2]?

Quote:

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Originally Posted by vikinginferno

Is it supposed to be d1+d2=10 for the first one where d1 is sq root[(x-4)^2+(y-11)^2]+ sq.root[(x-4)^2+(y+5)^2]?

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It is given that d1 + d2 = 10. So
sq root[(x-4)^2+(y-11)^2]+ sq.root[(x-4)^2+(y+5)^2] = 10
Or
sq root[(x-4)^2+(y-11)^2] = 10 - sq.root[(x-4)^2+(y+5)^2]
Square both the sides. Simplify. One sqrt remains in one side. Again square both the side to get the final result.
You have to the same thing for the second problem with one change. In that you have to find d1 - d2.