$k_y$

$X_1$

$|X_1F|=%v$

$|X_1r|=%v$

$X_2$

$|X_2F|=%v$

$|X_2r|=%v$

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

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

$\text{Point }X_1$

$\text{Point }X_2$

$|p|=%v$

$\text{Vertex }V$

$\text{Latus rectum }p$

$\text{Focus }F$

$\text{Axis }o$

$\text{Parabola }k_y$

$\text{Directrix }r$

\text{Parabola }p>0 

\text{Parabola }p<0 

\text{Change }p 

k_y:\ y=d+\frac{(x-c)^2}{2p}

$\text{Reflective property}$

p = 12 (slider from -15 to 15, step 0.1)
d = 1.5 (slider from -10 to 10, step 0.05)
r: y = d - p / 2
c = 2 (slider from -5 to 5, step 0.05)
F: (c, d + p / 2)
o = OrthogonalLine(F, r)
V: (c, d)
ky: y = d + (x - c)^(2) / 2 / p
X1 = Point(ky)
f = Segment(F, X1)
g = OrthogonalLine(X1, r)
A = Intersect(r, g)
h = Segment(X1, A)
X2 = Point(ky)
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(ky, s, 1)
t = Segment(E, F)
e = true
u = true
v = true
w = true
a_1 = true
b_1 = true
pp: 1 / 2 / p
text41: "k_y:\ y=" + (LaTeX[d]) + "+" + (LaTeX[pp]) + "(x-" + (LaTeX[c]) + ")^2"
text43: "k_y:\ y=" + (LaTeX[d]) + "+" + (LaTeX[pp]) + "x^2"
text46: "k_y:\ y=" + (LaTeX[d]) + "" + (LaTeX[pp]) + "x^2"
text44: "k_y:\ y=" + (LaTeX[d]) + "" + (LaTeX[pp]) + "(x-" + (LaTeX[c]) + ")^2"
cc: (-c)
text42: "k_y:\ y=" + (LaTeX[d]) + "+" + (LaTeX[pp]) + "(x+" + (LaTeX[cc]) + ")^2"
text45: "k_y:\ y=" + (LaTeX[d]) + "" + (LaTeX[pp]) + "(x+" + (LaTeX[cc]) + ")^2"
px: sqrt((15 * abs(p)))
q(x) = If[c - px ≤ x ≤ c + px, d + (x - c)^(2) / 2 / p]
L_4: (c - (4 * px / 5), q(c - (4 * px / 5)))
L_2: (c - (2 * px / 5), q(c - (2 * px / 5)))
LP: (c, q(c))
P_2: (c + (2 * px / 5), q(c + (2 * px / 5)))
P_4: (c + (4 * px / 5), q(c + (4 * px / 5)))
P_1: (c + px / 5, q(c + px / 5))
L_1: (c - px / 5, q(c - px / 5))
L_3: (c - (3 * px / 5), q(c - (3 * px / 5)))
P_3: (c + (3 * px / 5), q(c + (3 * px / 5)))
L_5: (c - px, q(c - px))
P_5: (c + px, q(c + px))
pv: (0, p)
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)