# Understanding Hyperbolas: When Objects Move Horizontally

• thecosmos123456
In summary, parabola and hyperbola are both defined by their mathematical shape, not by physical trajectories. However, hyperbolic trajectories do exist in space for objects traveling faster than the escape velocity of the orbited body. Gravity is the primary force acting on objects and can result in a hyperbolic trajectory for objects traveling at high speeds.
thecosmos123456
when an object is thrown horizontally ,after some time when the effect of the applied force is less than the effect of gravity then it changes its path and bends towards the Earth and the path is called a parabola ,then in the same sense how can we define hyperbola?

Parabola and hyperbola are defined by their mathematical shape, not by physical trajectories. They are both conic sections.

Why do you think there is a similar description for a hyperbola? I am not aware of any , though this of course does not mean there isn't one. But you can consider the physical aspects of parabolic mirrors/antennas and their reflecting properties.

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thecosmos123456 said:
when an object is thrown horizontally ,after some time when the effect of the applied force is less than the effect of gravity then it changes its path and bends towards the Earth and the path is called a parabola ,then in the same sense how can we define hyperbola?
I don't know if there is a terrestrial situation which results in a hyperbolic trajectory, but it is common to find hyperbolic orbits for bodies which are traveling faster than the escape velocity of the orbited body.

It's called an escape, or hyperbolic, trajectory:

https://en.wikipedia.org/wiki/Hyperbolic_trajectory

SammyS
thecosmos123456 said:
when an object is thrown horizontally ,after some time when the effect of the applied force is less than the effect of gravity then it changes its path and bends towards the Earth and the path is called a parabola ,then in the same sense how can we define hyperbola?
You're misunderstanding things here. Gravity doesn't act "after some time." If the object is thrown, the only force (and hence, the only acceleration) on the object is that due to gravity. If one object is dropped straight down, and another object is thrown horizontally, both object will cover the same vertical distance in the same amount of time.

If you could fire a bullet from a gun at about 25,100 mph (i.e. more than Earth's escape velocity which is 10x faster than bullets actually travel) and ignore air resistance, the bullet will follow (part of) an hyperbola.

The trajectory may depend on the object's initial condition and the net force it has during the whole process. The star's gravitation can make a hyperbola trajectory but it's not the way to define it.

## 1. What is a hyperbola?

A hyperbola is a type of conic section, formed by the intersection of a right circular cone and a plane that is parallel to one of the cone's generating lines. It has two branches, each of which resembles a curved "X" shape.

## 2. How do objects move horizontally on a hyperbola?

Objects on a hyperbola move horizontally at a constant velocity, with their speed increasing as they move away from the center of the hyperbola. This is due to the fact that the distance between the object and the center of the hyperbola decreases as the object moves away from the center.

## 3. What is the equation for a hyperbola?

The standard equation for a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center of the hyperbola and a and b are the lengths of the semi-major and semi-minor axes, respectively.

## 4. How does the eccentricity of a hyperbola affect its shape?

The eccentricity of a hyperbola is a measure of how "squished" or "stretched out" it is. The closer the eccentricity is to 1, the more elongated the hyperbola will be. As the eccentricity approaches 0, the hyperbola becomes more circular.

## 5. What are some real-life examples of hyperbolas?

Hyperbolas can be seen in various natural phenomena such as the paths of comets and the trajectories of objects in a gravitational slingshot. They can also be seen in man-made structures such as radio antennas and satellite dishes.

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