rgraphhyperbolic-function

Where did I go wrong in my attempt to graph a hyperbola using R?

The Task

Use R to plot the hyperbola x2 - y2/3 = 1, as in Figure 4.3:

enter image description here

My Attempt

x <- seq(-5, 5, by = 0.01)
x <- x[(3*(x^2 - 1)) >= 0]

y.upper <- sqrt(3*(x^2 - 1))
y.lower <- -sqrt(3*(x^2 - 1))
y.max <- max(y.upper)
y.min <- min(y.lower)
d1 <- sqrt(3)*x
d2 <- -sqrt(3)*x

plot(c(-5, 5), c(y.min, y.max), type = "n", xlab = "x", ylab = "y")
lines(x, y.upper)
lines(x, y.lower)
lines(x,d1)
lines(x,d2)
points(2, 0)
points(-2,0)
text(2, 0, "focus (2, 0)", pos=4)
text(5, y.max, "asymptote y = sqrt(3)*x", pos = 2)
title("The hyperbola x^2 - y^2/3 = 1")

enter image description here

As you can see, my graph has an extra line segment that shows up at y = 0 for x-values that should not have any result. I'm a bit confused as to what I did that resulted in such a graph.

Solution

  • Use of lines creates a continuous lines by joining the points. The two functions are for the upper and lower portions so they both connect points (-1, 0) and (1, 0).

    There are likely other ways to accomplish this, but the changes below show what's happening:

    plot(c(-5, 5), c(y.min, y.max), type = "n", xlab = "x", ylab = "y")
lines(x[x < 0], y.upper[x < 0])
lines(x[x > 0], y.upper[x > 0])
lines(x[x < 0], y.lower[x < 0])
lines(x[x > 0], y.lower[x > 0])
lines(x, d1)
lines(x, d2)
points(2, 0)
points(-2,0)
text(2, 0, "focus (2, 0)", pos=4)
text(5, y.max, "asymptote y = sqrt(3)*x", pos = 2)
title("The hyperbola x^2 - y^2/3 = 1")