Quadratic Curve
Definition
Plane curves of the following types that can be expressed by a quadratic equation in two variables are called conic sections.
Description
The Circle is a special case of the ellipse, so it is generally not mentioned separately when referring to conic sections.
Parabola
Ellipse
Hyperbola
Code
The following is Julia code for drawing conic sections.
using Plots
default(framestyle = :origin, color = :lightgray, lw = 2, legend = :none, ticks = [], size = [400, 400], aspect_ratio = 1)
t = range(-2, 2, length=100)
plot(t.^2, 2t)
vline!([-1], linestyle=:dash)
scatter!([1], [0], color = :black)
png("parabola.png")
θ = range(0, 2π, length=100)
plot(sqrt(2)*cos.(θ), sin.(θ))
scatter!([1, -1], [0, 0], color = :black)
png("ellipse.png")
plot()
plot!(cosh.(t), sinh.(t))
plot!(-cosh.(t), sinh.(t))
scatter!([sqrt(2), -sqrt(2)], [0, 0], color = :black)
png("hyperbola.png")