Question

Given 3 points, can one construct a hyperbolic curve thru them using classical geometry of straight edge and compass.

Answer 1

Answer on Question #37581 - <math> - <geometry>

Given 3 points, can one construct a hyperbolic curve thru them using classical geometry of straight edge and compass.

Solution:

Equation of the hyperbolic curve:

$$y = \frac {k}{x ^ {n} + b}$$

If we have three points on the hyperbolic curve $(\mathrm{A}(\mathrm{x}_1,\mathrm{y}_1);\mathrm{B}(\mathrm{x}_2,\mathrm{y}_2);\mathrm{C}(\mathrm{x}_3,\mathrm{y}_3))$ , we can substitute the value of $X$ and $Y$ of every point in the equation (1) and we will have three equations with three unknowns: $k,n,b$ . If we will solve the equation and find the unknown variables, it is possible to construct the hyperbolic curve using the equation (1) using known variables $k,n,b$ .

Answer: it is possible to construct hyperbolic curve through 3 given points.