Use complete sentences to describe how you can use inverse relationships to determine points on a hyperbola.

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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