This is not a question with an answer (as written). Given a point on the surface of the earth, there are infinitely many other points that are a given distance from the first, as long as the indicated distance is less than the diameter of the earth.
As well, you did not even state if that distance will be measured as the length of the arc of a great circle, or if it the distance is the length of a chord passing through the earth.
Anyway, asking for latitude and longitude has no meaning, since any point on a circle a given distance away has that specified distance.
