Find the angle between the two asymptotes of hyperbola?

Question

Answer

Angle between the Asymptotes of Hyperbola

A hyperbola is an open curve or shape that is formed by the intersection of a plane with a double cone. It has two asymptotes, which are straight lines that approach the curve but never touch it. The angle between the two asymptotes of a hyperbola is an important property that can be used to determine the shape and orientation of the curve.

Definition of Hyperbola

A hyperbola is defined as the set of all points in a plane such that the difference of the distances between any point on the curve and two fixed points (called the foci) is constant. The two foci of a hyperbola are located on the major axis, which is the axis that passes through the two vertices of the curve.

Equation of Hyperbola

The standard equation of a hyperbola is given by:

(x - h)²/a² - (y - k)²/b² = 1

where (h, k) is the center of the hyperbola, a is the distance from the center to each vertex along the major axis, and b is the distance from the center to each co-vertex along the minor axis.

Asymptotes of Hyperbola

The asymptotes of a hyperbola are two straight lines that intersect at the center of the curve. They are defined by the equation:

y - k = ±(b/a)(x - h)

where (h, k) is the center of the hyperbola, a is the distance from the center to each vertex along the major axis, and b is the distance from the center to each co-vertex along the minor axis.

Angle between the Asymptotes

The angle between the two asymptotes of a hyperbola is given by:

θ = tan⁻¹(b/a)

where a and b are the distances from the center of the hyperbola to the vertices and co-vertices along the major and minor axes, respectively.

Conclusion

Therefore, the angle between the two asymptotes of a hyperbola is determined by the ratio of the distance from the center to the co-vertices to the distance from the center to the vertices along the major axis. This property can be used to determine the shape and orientation of the curve, and is an important tool in the study of hyperbolas and other conic sections.

Answer

I think its 90

Answer

2 tan arc b/a

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