$k_x$

$k_x$

$X_1$

$|X_1F|=%v$

$|X_1r|=%v$

$X_2$

$|X_2F|=%v$

$|X_2r|=%v$

$\frac{|p|}{2}$

$\frac{|p|}{2}=%v$

$\text{Point }X_1$

$\text{Point }X_2$

$|p|=%v$

$\text{Vertex }V=[c,d]$

$\text{Latus rectum }p$

$\text{Focus }F$

$\text{Axis }o$

$\text{Parabola }k_y$

$\text{Directrix }r$

\text{Parabola }p>0 

\text{Parabola }p<0 

\text{Change }p 

k_x:\ y=d\pm\sqrt{2p(x-c)}

$\text{Reflective property}$

c = -0.5 (slider from -5 to 5, step 0.05)
p = 3.2 (slider from -15 to 15, step 0.1)
r: x = c - p / 2
d = 1 (slider from -10 to 10, step 0.05)
F: (c + p / 2, d)
e_1 = If(abs(p) > 0, Parabola[F, r])
ky(x) = d - sqrt(((2 * p) * (x - c)))
o = OrthogonalLine(F, r)
V: (c, d)
kx(x) = d + sqrt(((2 * p) * (x - c)))
X1 = Point(e_1)
f = Segment(F, X1)
g = OrthogonalLine(X1, r)
A = Intersect(r, g)
h = Segment(X1, A)
X2 = Point(e_1)
i = Segment(X2, F)
j = OrthogonalLine(X2, r)
B = Intersect(r, j)
k = Segment(X2, B)
n = Segment(F, V)
C = Intersect(r, o)
m = Segment(V, C)
a = false
b = false
s = OrthogonalLine(F, o)
E = Intersect(kx, s, 1)
t = Segment(E, F)
e = true
u = true
v = true
w = true
a_1 = true
b_1 = true
pp: (2 * p)
cc: (-c)
px: sqrt((15 * abs(p)))
q(x) = If[c - px ≤ x ≤ c + px, d + (x - c)^(2) / 2 / p]
L_4: (c + (3 * sgn(p)), ky(c + (3 * sgn(p))))
L_2: (c + sgn(p), ky(c + sgn(p)))
LP: (c, d)
P_2: (c + sgn(p), kx(c + sgn(p)))
P_4: (c + (3 * sgn(p)), kx(c + (3 * sgn(p))))
P_1: (c + (0.5 * sgn(p)), kx(c + (0.5 * sgn(p))))
L_1: (c + (0.4 * sgn(p)), ky(c + (0.4 * sgn(p))))
L_3: (c + (2 * sgn(p)), ky(c + (2 * sgn(p))))
P_3: (c + (2 * sgn(p)), kx(c + (2 * sgn(p))))
L_5: (c + (4 * sgn(p)), ky(c + (4 * sgn(p))))
P_5: (c + (4 * sgn(p)), kx(c + (4 * sgn(p))))
pv: (p, 0)
hd = Ray(LP, pv)
h_5 = Ray(L_5, pv)
h_4 = Ray(L_4, pv)
h_3 = Ray(L_3, pv)
h_2 = Ray(L_2, pv)
h_1 = Ray(L_1, pv)
d_5 = Ray(P_5, pv)
d_4 = Ray(P_4, pv)
d_3 = Ray(P_3, pv)
d_2 = Ray(P_2, pv)
d_1 = Ray(P_1, pv)
c_1 = false
l_1 = Segment(L_1, F)
l_2 = Segment(L_2, F)
l_3 = Segment(L_3, F)
l_4 = Segment(L_4, F)
l_5 = Segment(L_5, F)
lp = Segment(LP, F)
p_1 = Segment(P_1, F)
p_2 = Segment(P_2, F)
p_3 = Segment(P_3, F)
p_4 = Segment(P_4, F)
p_5 = Segment(P_5, F)
r_1: y = d - p / 2
F_1: (c, d + p / 2)
text41: "k_x:\ y=" + (LaTeX[d]) + "\pm\sqrt{" + (LaTeX[pp]) + "(x-" + (LaTeX[c]) + ")}"
text43: "k_x:\ y=" + (LaTeX[d]) + "\pm\sqrt{" + (LaTeX[pp]) + "x}"
text42: "k_x:\ y=" + (LaTeX[d]) + "\pm\sqrt{" + (LaTeX[pp]) + "(x+" + (LaTeX[cc]) + ")}"
L_0: (c + (0.1 * sgn(p)), ky(c + (0.1 * sgn(p))))
P_0: (c + (0.1 * sgn(p)), kx(c + (0.1 * sgn(p))))
d_0 = Ray(P_0, pv)
h_0 = Ray(L_0, pv)
l_0 = Segment(L_0, F)
p_0 = Segment(P_0, F)