Can anybody explain if the reciprocal cone of the cone touching the three axes will be the cone touching the three coordinate planes. If yes, why?
$3$-D diagram would really help if possible. Thanks.
2026-03-25 05:59:12.1774418352
Reciprocal Cone
1k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ANALYTIC-GEOMETRY
- Asymptotes of hyperbola
- Position of point with respect to hyperbola
- Length of Shadow from a lamp?
- Show that the asymptotes of an hyperbola are its tangents at infinity points
- Surface by revolution
- All possible values of coordinate k such that triangle ABC is a right triangle?
- Triangle inside triangle
- Is there an equation to describe regular polytopes?
- How do I prove that the gradient between a fixed and any general point on a given line is $m$?
- Three-Dimensional coordinate system
Related Questions in 3D
- Visualization of Projective Space
- Approximate spline equation with Wolfram Mathematica
- Three-Dimensional coordinate system
- Volume of sphere split into eight sections?
- Largest Cube that fits the space between two Spheres?
- Is $ABC$ similar with $A'B'C'$, where $A', B', C'$ are the projections of $A, B, C $ on a plane $\pi $.
- Intersection of a facet and a plane
- Distance from center of sphere to apex of pyramid?
- Looking for hints on the below 3D geometry problem.
- Finding the Euler angle/axis from a 2 axes rotation but that lies on the original 2 axes' plane
Related Questions in QUADRICS
- Conditions for a plane and an ellipsoid NOT to intersect
- Prove that three paraboloids have a common tangent plane
- Calculate centres of a quadric
- Quadric represented in matrix form
- Volume without Multivariable Calculus
- Cone $x^2+y^2-z^2=0$ as a degenerate quadric
- Normal form for quadrics
- Intersection of two smooth projective quadrics in general position
- Vertex and axis of $n$-dimensional paraboloid
- Canonic form of a quadric
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It turned out that the reciprocal cone is just what you get taking the inverse of the symmetric matrix that defined the first cone. I gave a big answer at condition for cones to be reciprocal
I'm not going to post any diagrams.
The "cone touching the three axes" is $$ yz + zx + xy = 0. $$ The matrix can be the Hessian matrix of second partial derivatives of the quadratic form. The basic rule is that the Hessian matrix have determinant not equal to zero.