Vnitřní oblast elipsy

X

Y

T

Přímka je tečnou elipsy. 
Má s elipsou společný
právě jeden bod T.

Přímka je sečnou elipsy.
Má s elipsou společné
dva různé body X,Y.

Přímka je vnější přímkou elipsy.
Nemá s elipsou společný
žádný bod.

Pohybujte posuvníkem

c = 12.5 (slider from -9 to 12.5, step 0.1)
b: x - 2 * y + c = 0
A, B = Intersect(c_1, b)
C = Point(xAxis)
a = OrthogonalLine(C, xAxis)
E = Point(a)
F = Point(a)
text8: "p:" + (LaTeX[b]) + "\\k:" + (LaTeX[c_1]) + ""
d: c / 2
text9: "Dosazení \\2x^2+(0.5x" + (LaTeX[d]) + ")^2-8x-4(0.5x" + (LaTeX[d]) + ")=6"
k: 0.5 * c - 10
l: d^(2) - 4 * d - 6
text10: "2.25x^2" + (LaTeX[k]) + "x+" + (LaTeX[l]) + "=0"
text12: "2.25x^2" + (LaTeX[k]) + "x" + (LaTeX[l]) + "=0"
D: k^(2) - 9 * l
text13: "D = " + D + ""
x_1: x(A)
x_2: x(B)
y_1: y(A)
y_2: y(B)
text14: "x_{1}=" + (LaTeX[x_1]) + "⇒y_{1}=" + (LaTeX[y_1]) + "\\x_{2}=" + (LaTeX[x_2]) + "⇒y_{2}=" + (LaTeX[y_2]) + ""
text15: "X=\left [ " + (LaTeX[x_1]) + "," + (LaTeX[y_1]) + "  \right ] \\Y=\left [ " + (LaTeX[x_2]) + "," + (LaTeX[y_2]) + " \right ] "
text16: "x=" + (LaTeX[x_1]) + "⇒y=" + (LaTeX[y_1]) + ""
text17: "T=\left [" + (LaTeX[x_1]) + "," + (LaTeX[y_1]) + "  \right ] "
G = Point(b)
H = Intersect(b, a)
I = (-6.177359157424641, 6.283430716401504)
e = Segment(G, H)
text11: "Dosazení \\ 
2x^2+(0.5x+" + (LaTeX[d]) + ")^2-8x-4(0.5x+" + (LaTeX[d]) + ")=6"