Calc Vertice Problem: Finding the Closest Point in an Ellipse to a Focus

  • Thread starter flyingpig
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In summary, a "Calc Vertice Problem" is a mathematical problem involving finding the closest point in an ellipse to one of its focuses. It can be solved using algebraic methods or computer programs, and has applications in fields such as physics and engineering. The significance of finding this point lies in its real-life applications, such as predicting the trajectory of a projectile or designing satellite orbits. Examples of Calc Vertice Problems can be found in astronomy, ballistics, and navigation. Some common challenges when solving these problems include accurately representing the ellipse and its properties, as well as understanding complex mathematical concepts.
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flyingpig
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Homework Statement



One vertice is the closest point to a focus in an ellipse. For instance take

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex] with a > b > 0 and one focus at (c,0) and one vertice at (a,0), is (a,0) the closest point on the ellipse to the focus (c,0)?


2. The attempt at a solution

This is true right?
 
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  • #2
Yes, that is true. And the other vertex, (-a, 0) is the point farthest from the focus.

By the way, the singular of "verices" is "vertex", not "vertice".
 

What is a "Calc Vertice Problem"?

The "Calc Vertice Problem" refers to a mathematical problem that involves finding the closest point in an ellipse to one of its focuses. This problem is often encountered in fields such as physics and engineering.

How do you solve a Calc Vertice Problem?

To solve a Calc Vertice Problem, you will need to use mathematical equations and concepts such as the distance formula and the properties of an ellipse. This problem can be solved using algebraic methods or with the help of computer programs.

What is the significance of finding the closest point in an ellipse to a focus?

The closest point in an ellipse to a focus is known as the vertex or the focus of the ellipse. This point has important applications in real-life scenarios, such as predicting the trajectory of a projectile or designing satellite orbits.

Are there any real-life examples of Calc Vertice Problems?

Yes, Calc Vertice Problems can be found in various fields such as astronomy, ballistics, and navigation. For example, in astronomy, the closest point in an elliptical orbit to the sun is the point of perihelion, which is important for studying the motion of planets.

What are some common challenges when solving Calc Vertice Problems?

One of the main challenges when solving Calc Vertice Problems is accurately representing the ellipse and its properties. Additionally, the calculations involved can be complex and require a thorough understanding of mathematical concepts.

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