Check whether the conicoid central or not

  • MHB
  • Thread starter debrajr
  • Start date
In summary, the conversation discusses the task of determining whether a given conicoid is central or not. If it is central, the center and the conics formed by its intersection with the coordinate planes must be obtained. If the conicoid is not central, all its tangent planes parallel to the coordinate planes must be found.
  • #1
debrajr
4
0
Check whether the conicoid represented by
\(\displaystyle 3x^2-5y^2+z^2-6xy+7yz=15\)
is central or not.

If it is central, obtain the center and the conics given by the intersection of the conicoid with the coordinate planes.

If the given conicoid is not central, obtain all its tangent planes parallel to the coordinate planes.
 
Mathematics news on Phys.org
  • #2
Hello debrajr and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

FAQ: Check whether the conicoid central or not

What is a conicoid?

A conicoid is a three-dimensional geometric figure that is created by rotating a conic section (such as a circle, ellipse, parabola, or hyperbola) around its axis.

How do I determine if a conicoid is central?

A conicoid is considered central if its axis of rotation is perpendicular to the plane of the base conic section.

What tools are needed to check if a conicoid is central?

You will need a ruler or measuring tape to determine the axis of rotation and a protractor to measure the angle between the axis and the base conic section.

Can a conicoid be both central and non-central?

No, a conicoid can only be classified as either central or non-central. If the axis of rotation is not perpendicular to the base conic section, it is considered non-central.

Why is it important to know if a conicoid is central or not?

Determining if a conicoid is central is important because it affects the geometric properties of the figure, such as the shape and orientation of cross-sections. It also helps in solving problems involving conicoids, such as finding the volume or surface area.

Similar threads

Understanding Conic Sections: Exploring the Plane-Cone Intersection
Replies
1
Views
3K
I Possible simple formula for ellipse circumference
Replies
6
Views
2K
MHB Logical error in Spivak's Calculus?
Replies
2
Views
3K
What is the equation of a circle
Replies
1
Views
2K
MHB Most efficient way to identify a circle
Replies
6
Views
3K
MHB How Does Angular Velocity Affect a Block on a Rotating Wedge?
Replies
12
Views
4K
I Did I figure-out z-translation of 2D-coordinates correctly?
Replies
4
Views
437
Find intersections between sphere and parallel tangent planes
Replies
7
Views
2K
Lagrange multipliers understanding
Replies
8
Views
1K
Vector Equation of Plane w/ (-2,2,1) & Parallels (1,1,2) and (2,1,-1)
Replies
1
Views
864

Hot Threads

Recent Insights

Back
Top