Geometric locus of points. The vertices of triangles having a common base and congruent altitudes.
I came up with the picture below.

I we consider the segment AB as our common base, and all altitudes length congruent the segment CB, then the geometric locus of points is the line HC and IJ. Is this correct? I came up with two sets of points which are the two lines. But I thought the geometric locus of points is a unique set of points that satisfy some condition. But the two lines I got satisfy the given condition but not unique.
André already pointed out the key aspect in his comments, but I'd like to get this question out of the unanswered queue.

The locus is the set of all points satisfying given constraints. In your case, any point on either of the two (infinite) lines will satisfy the requirements, as you already pointed out yourself. Therefore the locus is the union of all these points, i.e. the union of the two lines you described. So the locus consists of both lines taken together. As such it is unique.
Andre and MvG already answered this question very well. But still I want to add something from the Master Euclid:

If you study the Proposition 37 of Euclid's Book 1, it directly relates to this question. His proposition states that "Triangles which are on the same bases and between the same parallels (lines) are equal to one another."

You may be worried about the converse of this theorem. But its converse really holds true. If you like to further investigate the converse or related theorems, please see this https://mathematicshub.wordpress.com/2015/08/29/proposition-37-euclids-elements/.

Also, this is a question, that I saw in the Kiselev's Geometry Book 1 as question number 199. I've solved a lot of questions from this book. I also want someone who is interested in matching the answers of the questions as the author never wrote any solution manual.