Two Coast Guard radio towers can locate a distressed boat from the difference in signal arrival times — the boat sits somewhere on an invisible hyperbola. In plain words, a hyperbola is the set of points where the difference of the distances to two foci stays constant, and its standard equation is x²/a² − y²/b² = 1. The focal distance comes from c = √(a² + b²): square both semi-axes, add, and take the root. With a = 3 and b = 4, the foci sit 5 units from the center. Students graphing conic sections, navigators using old LORAN signals, and physicists tracing a comet's escape path all meet this curve. It is the ellipse's rebellious sibling — the minus sign between the squares changes everything.

This calculator finds the focal distance. Type the semi-axis a into the Variable A box, say 3, and the semi-axis b into the Variable B box, say 4. Read c from the Result box: 5. Square the result to verify — 25 should equal 9 + 16 — and remember that c is always larger than both a and b on a hyperbola.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Hyperbola Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.