Angle between tangent and foci. (Involve vector calculus)

In summary, the angle between a tangent line and a foci point is known as the tangent angle and can be calculated using vector calculus. It is directly related to the eccentricity of an ellipse and can be negative if the tangent line intersects the foci vector in the opposite direction. The tangent angle can also be used to determine the orientation of an ellipse and has practical applications in fields such as astronomy and engineering.
  • #1
athrun200
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Homework Statement


See the photo on the left


Homework Equations





The Attempt at a Solution


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  • #2
You must show some work of your own or this thread will be deleted.
 
  • #3
In fact, I type my work on the computer, the photo I have shown is already my work.
That is not solution, that is my attempt to solution. So it may be wrong.
 
Last edited:

1. What is the angle between a tangent line and a foci point?

The angle between a tangent line and a foci point is known as the tangent angle. It is the angle formed between the tangent vector and the foci vector, and it can be calculated using vector calculus.

2. How is the tangent angle related to the eccentricity of an ellipse?

The tangent angle is directly related to the eccentricity of an ellipse. As the eccentricity increases, the tangent angle also increases and approaches 90 degrees. When the eccentricity is 0, the ellipse is a circle and the tangent angle is 0 degrees.

3. Can the tangent angle be negative?

Yes, the tangent angle can be negative. This occurs when the tangent line intersects the foci vector in the opposite direction, resulting in an angle between 180 and 360 degrees. In vector calculus, negative angles are often represented as angles greater than 180 degrees.

4. How can the tangent angle be used to determine the orientation of an ellipse?

The tangent angle can be used to determine the orientation of an ellipse by looking at the direction of the tangent vector. If the tangent vector is pointing towards the foci, the ellipse is said to be prograde. If the tangent vector is pointing away from the foci, the ellipse is said to be retrograde.

5. Are there any real-world applications of the angle between tangent and foci?

Yes, there are many real-world applications of the angle between tangent and foci. For example, in astronomy, the tangent angle can be used to determine the orientation and shape of planetary orbits. In engineering, it can be used to calculate the direction and force of pressure on objects moving in an elliptical path.

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