Hyperbolic Graph

 A hyperbola can be defined in multiple ways

1) Using two points

A hyperbola is a set of points, such that for any point \(P\) of the set, the absolute difference of the distances from two points, \(F_1\) and \(F_2\), is constant \[||PF_1|-|PF_2|| = 2a\] \(a\) is the distance from the midpoint to the vertices, \(V_1\) and \(V_2\). The hyperbola has asymptotes at \[y = ± \frac{b}{a}x\]

Hyperbolic Curve. Drag the shaded blue circles to adjust the parameters.

2) Using a circle and a point

If \(c_2\) is the circle with midpoint \(F_2\) and radius \(2a\),then the distance of a point \(P\) of the right branch of the hyperbola to the circle \(c_2\) equals the distance to the focus \(F_1\). If \(N\) is the point on \(c_2\) this can be written:\[|NP| = |PF_1|\] \(c_2\)is called the circular directrix (related to focus \(F_2\)) of the hyperbola

Hyperbolic Curve. Drag the shaded green circle to adjust the parameters.