WOLFRAM|DEMONSTRATIONS PROJECT

Tangent Lines to a Conic Section

​
conic section
ellipse: A
2
x
+C
2
y
+x+y-300,
2
B
-4AC<0
A
2
B
2
C
1.3
x
0
conic section:
2
2
x
+x+1.3
2
y
+y-300
tangent line at (
0
,
-5.20383
) :
x-12.53y-65.20380
Suppose that
(
x
0
,
y
0
)
is a point on the conic section
A
2
x
+Bxy+C
2
y
+Dx+Ey+F=0
. Then the tangent line to the conic section at point
(
x
0
,
y
0
)
is
(2A
x
0
+B
y
0
+D)x+(B
x
0
+2C
y
0
+E)y-A
2
x
0
-B
x
0
y
0
-C
2
y
0
+F=0.