Hyperbolic Sector Area Calculator

Find the area of a hyperbolic sector of x²/a²−y²/b²=1 from the semi-axes a and b and the parameter t or a point on the curve. Area = (a·b/2)·t.

Input

Enter the semi-axes a and b of the hyperbola x²/a²−y²/b²=1 and either the hyperbolic angle (parameter t) or a point on the curve to find the sector area.

Semi-axis a

Semi-axis b

Hyperbolic angle t

The point becomes (a·cosh t, b·sinh t).

Result

Sector area

Parameter t

Point x

3.086161

Point y

1.175201

The area bounded by the origin, the vertex and the point (a·cosh t, b·sinh t) on the curve is A = (a·b ÷ 2)·t.

How it works

A point on the hyperbola can be written as (a·cosh t, b·sinh t).
The sector bounded by the origin, the vertex (a,0) and that point has area A = (a·b/2)·t.
In point mode the parameter is recovered as t = arccosh(x ÷ a). The x of the point must be at least a.
Enter positive numbers for a and b.

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