Hyperbola in Cartesian Planes problem (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

362
0
Does the plane that intersects the cone need to be parallell to the axis of the cone to make the section a hyperbola, or is it enough that it is not parallell to a generator?

If the latter is correct, can one say that a parabola is a special case of a hyperbola?
 
Last edited:

Gib Z

Homework Helper
3,345
2
The Latter is correct.

The hyperbola in Cartesian Planes is defined by Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. As you Can see, a parabola is simply where B and C equals zero.
 
362
0
Thank you!
 

Gib Z

Homework Helper
3,345
2
No problemo :)
 

dextercioby

Science Advisor
Homework Helper
Insights Author
12,905
494
If one takes one of the focal points of a hyperbola to infinity, then the remaining curve would be a parabola. Same is valid for an ellipse.

In other words let b tend to infinity in

[tex] \frac{x^{2}}{a^{2}}\pm \frac{y^{2}}{b^{2}} =1 [/tex]

and you'll get a parabola.

Daniel.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top