The set of points that form a hyperbola are inversely related.
Two variables, A and B are inversely proportional if A is equal to a constant, K, divided by B, i.e. A = K/ B. That, of course is equivalent that B = K/A, which means that if the two variables are inversely related, A in inverselty proportional to A and B is inversely proportional to A, with the same inverse proportion constat.
Then, if you have two points of the hyperpola, you can find the constant of proportion K, by using K = A*B.
Once you have the constat K, you can find all the points of the hyperbola by plugging any value of B' to determine A, by doing A' = K / B'.
If you know that the points 4 and 12 are inversely related, you find the constant k , by doing k = 4-12 = 48, and now you can generate the points of the parabola by doing>
A = 48/B or B = A/48
So, using A = 48/B, you can find all the values of A for any value of B and those points form a hyperboly.
B A
1 48/1 = 48
2 48/2 = 24
3 48/3 = 16
4 48/4 = 12
-1 -48
-2 -24
-3 -16
-4 -12
Draw those points in a coordinate system and you will see a hyperbola.
quantities that are inversely related