Parábola, Elipse e Hipérbole

Exemplos

library(rootSolve)
x0 <- 1
y0 <- 2
a <- 3
b <- 4
m <- round((b/a), digits = 2)
c <- sqrt((a^2)+(b^2))

fx <- function(x){
  (b^2)*((x^2)/(a^2) - 1)
}


raiz <- multiroot(f = fx, start = c(-10,10))
limInf <- raiz$root[1]
limSup <- raiz$root[2]


x_left <- seq(-10, limInf, by = 0.001)
x_right <- seq(limSup, 10, 0.001)

y.upper_left <- sqrt((b^2)*((x_left^2)/(a^2) - 1))
y.upper_right <- sqrt((b^2)*((x_right^2)/(a^2) - 1))
y.lower_left <- -sqrt((b^2)*((x_left^2)/(a^2) - 1))
y.lower_right <- -sqrt((b^2)*((x_right^2)/(a^2) - 1))
y.max <- max(y.upper_left)
y.min <- min(y.lower_left)

plot(c(-10, 10), c(y.min, y.max), type = "n", xlab = "x", ylab = "y")
lines(x_left, y.upper_left, col = "red", lwd = 2)
lines(x_right, y.upper_right, col = "red", lwd = 2)
lines(x_left, y.lower_left, col = "red", lwd = 2)
lines(x_right, y.lower_right, col = "red", lwd = 2)
abline(0, m, col = "blue")
abline(0, -m, col = "blue")
points(c, 0, pch = 20)
points(-c,0, pch = 20)
text(c/2, 1, paste0("Foco (",round(c, digits = 2),",0)"), pos=4)
text(-c-c/2, 1, paste0("Foco (",round(-c, digits = 2),",0)"), pos=4)

text(c, y.max, bquote("Assintota" ~ .(m)*x), pos = 2)
title(bquote("Hipérbole "~(x^2)/(.(a))^2 - (y^{2})/(.(b))^2==1))

Parábolas

#Caso 1
#O eixo da parabola eh o eixo y
#Nesse caso F(0,P/2) e o vertice passa pela origem do eixo y
#P eh um ponto qq da parabola

v=0
p <- 2

if(p<0){
  curve(((x^2)/(2*p)), 
        from = -8, 
        to = 8,
        col = "black", 
        lty = 1, 
        lwd = 2,
        ylab = "y",
        ylim=c(10*p,-10*p),
        xlim = c(-10,10))
}else{
  curve(((x^2)/(2*p)), 
        from = -8, 
        to = 8,
        col = "black", 
        lty = 1, 
        lwd = 2,
        ylab = "y",
        ylim=c(-10*p,10*p),
        xlim = c(-10,10))
}
abline(h=-(p/2), 
       lwd = 2, 
       lty = 2)
abline(h=0, 
       lwd = 2, 
       lty = 3)
points(x = 0, y = p/2, pch = 16,
       col = "black")
text("F", x=0, y=((p/2)+2))
text("V", x=5, y=1)
grid(nx = NULL, ny = NULL,
     lty = 2,      # Grid line type
     col = "gray", # Grid line color
     lwd = 1)      # Grid line width)

h <- 2
k <- -1
p <- 8

y <- function(x){
  return((((x-h)^2)/(2*p))+k)
}

limInf <- h-5
limSup <- h+5

if(p<0){
  curve(y, 
        from = limInf, 
        to = limSup,
        col = "black", 
        lty = 1, 
        lwd = 2,
        ylab = "y",
        ylim=c(y(limSup)-3,y(h)+3),
        xlim = c((h-6),(h+6)))
}else{
  curve(y, 
        from = limInf, 
        to = limSup,
        col = "black", 
        lty = 1, 
        lwd = 2,
        ylab = "y",
        ylim=c((y(h)-3),y(limSup)+3),
        xlim = c((h-6),(h+6)))
}
abline(h=k, 
       lwd = 2, 
       lty = 2)
abline(h=0, 
       lwd = 2, 
       lty = 3)
points(x = h, y = ((p/2)+k), pch = 16,
       col = "black")
text("F", x=h, y=(((p/2)+k)+0.1))
text("V", x=5, y=1)
grid(nx = NULL, ny = NULL,
     lty = 2,      # Grid line type
     col = "gray", # Grid line color
     lwd = 1)      # Grid line width)