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Original file (SVG file, nominally 630 × 630 pixels, file size: 104 KB)
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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 |
 |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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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()
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:42, 22 March 2024 | | 630 × 630 (104 KB) | Melikamp | better green |
| 17:52, 21 March 2024 |  | 630 × 630 (104 KB) | Melikamp | Uploaded own work with UploadWizard |
File usage
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Global file usage
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- Usage on uk.wikipedia.org
