# conicAsymptotes: Asymptotes of a conic In conics: Plot Conics

## Description

Find the slopes of the asymptotic directions of a conic.

## Usage

 `1` ``` conicAsymptotes(x) ```

## Arguments

 `x` a 6-length vector or a symmetric 3x3 matrix

## Details

The `conicAsymptotes` function calculates the slopes of the asymptotic directions of a conic specified by its coefficients or by its symmetric matrix.

If the equation of the conic is

 `1` ``` v_1 x_1^2 + v_2 x_1x_2 + v_3 x_2^2 + v_4 x_1 + v_5 x_2 + v_6 = 0 ```

the slopes of the asymptotes are the roots of the equation at infinity of the conic:

 `1` ``` v_1 + v_2 t + v_3 t^2 = 0 ```

where `t=x_2/x_1`.

## Value

A vector containing the slopes: two values in the case of a hyperbola or of intersecting lines, one value in the case of a parabola or of parallel lines. In the case of an ellipse (which has no points at infinity), the function returns an empty vector.

## Author(s)

Bernard Desgraupes
[email protected]
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

`conicAxes`, `conicCenter`, `conicMatrix`, `conicPlot`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```# Hyperbola # Equation: 2*x_1^2 + 2*x_1*x_2 - 2*x_2^2 - 20*x_1 + 20*x_2 + 10 = 0 v <- c(2,2,-2,-20,20,10) conicAsymptotes(v) # Ellipse # Equation: 2*x_1^2 + 2*x_1*x_2 + 2*x_2^2 - 20*x_1 - 28*x_2 + 10 = 0 v <- c(2,2,2,-20,-28,10) # Should return an empty vector (an ellipse has no asymptotes!): conicAsymptotes(v) ```