File:Conjugate-unit-hyperbolas.svg
Summary
| Description |
English: The rectangular hyperbola x^2 - y^2 and its conjugate, having the same asymptotes. |
| Date | |
| Source | Own work |
| Author | Melikamp |
| Other versions |
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Licensing
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R code
library(svglite)
svg("conjugate-unit-hyperbolas.svg")
r = 4 # max |x| and |y|
res = 100 # plotting resolution per unit
colg = "gray"
colx = "springgreen4"
coly = "royalblue"
cola = "red"
par(mar = c(3, 3, 1, 1))
plot.new()
plot.window(c(-r, r), c(-r, r))
# axes
axis(1, -r:r)
axis(2, -r:r)
mtext("x", side=1, line=2)
mtext("y", side=2, line=2)
# grid
abline(h = -r:r, lty=3, col=colg)
abline(v = -r:r, lty=3, col=colg)
# asymptotes
abline(0, 1, lty=3, col=cola, lwd=1.5)
abline(0, -1, lty=3, col=cola, lwd=1.5)
# curves
x = (((-r-0.2)*res):((r+0.2)*res))/res
lines(x, sqrt(1+x^2), col=colx, lwd=3)
lines(x, -sqrt(1+x^2), col=colx, lwd=3)
lines(sqrt(1+x^2), x, col=coly, lwd=3)
lines(-sqrt(1+x^2), x, col=coly, lwd=3)
# labels
text(-0.2, 2.5, expression("x"^2 - "y"^2 == -1), cex=2.3, col=colx)
text(2.7, -0.5, expression("x"^2 - "y"^2 == 1), cex=2.3, col=coly)
text(0, -0.8, "asymptotes", col=cola)
dev.off()