Rectangular Hyperbola

Rectangular Hyperbola

Hyperbolas where the semiaxes are equal are called rectangular or equilateral hyperbolas (a = b).

The equation of a rectangular hyperbola is:

Rectangular Hyperbola Equation

The equations of the asymptotes are:

Asymptotes Equation, Asymptotes Equation

That is, the angle bisectors of the quadrants.

The eccentricity is: Eccentricity

Equation of a Rectangular Hyperbola

Equilateral Hyperbola Rotated Rectangular Hyperbola

To switch the asymptotes to those determined by the x and y-axis, turn the asymptote −45° about the origin.

Rectangular Hyperbola

Rotated Rectangular Hyperbola

If it is rotated 45°, the hyperbola is in the second and fourth quadrant.

Rotated Rectangular Hyperbola

Example

Calculate the vertices and foci of a rectangular hyperbola of equation Rectangular Hyperbola Example.

The coordinates of the vertices are on the bisector of the first and third quadrant and the first and second coordinate coincide, that is to say, x = y. Also, Point A belongs to the curve of the hyperbola.

Rectangular Hyperbola Exercise

Rectangular Hyperbola Calculations

The length of the semi-axis, a, is the distance from the origin to Vertex A.

Rectangular Hyperbola Calculations

Rectangular Hyperbola Calculations

Rectangular Hyperbola Calculations

The length of the semi-axis, c, is the distance from the origin to Point C.

Rectangular Hyperbola Calculations

Rectangular Hyperbola Solution

Rectangular Hyperbola Calculations





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