The Conics

[mathdad]

The parabola is part of the conics section in analytic geometry. Name the other three parts.

•ellipse
•hyperbola
•circle

How important is this idea to the study of single and multivariable calculus?

 

[JeffM]

The conic sections represent relations between the squares of two variables or between one variable and the square of another. Thus, they are relatively simple relations to understand. For example, the very simple relation represented algebraically by

[MATH]y = \dfrac{k}{x} \text {, where } k \ne 0[/MATH]
is represented geometrically by a hyperbola.

Moreover, the relations represented by the conic sections arise frequently in nature. For example, the motion of an object under a gravitational force (absent friction or other complicating factors) is described either by a parabola or an ellipse.

As for the theory behind calculus, the conic sections are irrelevant.

 

[mathdad]

The conic sections represent relations between the squares of two variables or between one variable and the square of another. Thus, they are relatively simple relations to understand. For example, the very simple relation represented algebraically by

[MATH]y = \dfrac{k}{x} \text {, where } k \ne 0[/MATH]
is represented geometrically by a hyperbola.

Moreover, the relations represented by the conic sections arise frequently in nature. For example, the motion of an object under a gravitational force (absent friction or other complicating factors) is described either by a parabola or an ellipse.

As for the theory behind calculus, the conic sections are irrelevant.

An interesting read. Thank you. Back in my student days, the conic sections were intimidating as presented in textbooks.

 

[Otis]

...
•ellipse
•hyperbola
•circle
...

? A circle is an ellipse, in the same sense that a Real number is a Complex number and an equilateral triangle is an isosceles triangle.

In other words, each of those objects is a special case of the larger family listed. Cheers

?

 

[mathdad]

? A circle is an ellipse, in the same sense that a Real number is a Complex number and an equilateral triangle is an isosceles triangle.

In other words, each of those objects is a special case of the larger family listed. Cheers

?

I get it.