∆ = x (t) y (t) x (t) y (t) . sx(t) = x(t) − y (t) [x (t)]2 + [y (t)]2 ∆ , sy(t) = y(t) +

∆ = x (t) y (t) x (t) y (t) . sx(t) = x(t) − y (t) [x (t)]2 + [y (t)]2 ∆ , sy(t) = y(t) +

x0 (t) y 0 (t)
∆=
x00 (t) y 00 (t)
.
[x0 (t)]2 + [y 0 (t)]2
,
∆
[x0 (t)]2 + [y 0 (t)]2
0
sy (t) = y(t) + x (t)
,
∆
1
|∆|
=q
3.
ρ(t)
[x0 (t)]2 + [y 0 (t)]2
sx (t) = x(t) − y 0 (t)
v
u
u ([x0 (t)]2 + [y 0 (t)]2 + [z 0 (t)]2 )([x00 (t)]2 + [y 00 (t)]2 + [z 00 (t)]2 ) − (x0 (t)x00 (t) + y 0 (t)y 00 (t) + z 0 (t)z 00 (t))
1
=t
.
ρ(t)
([x0 (t)]2 + [y 0 (t)]2 + [z 0 (t)]2 )3
x0 (t) y 0 (t) z 0 (t)
x00 (t) y 00 (t) z 00 (t)
x000 (t) y 000 (t) z 000 (t)
T =
([x0 (t)]2 + [y 0 (t)]2 + [z 0 (t)]2 )3
[ρ(t)]2 · x0 (t)(x − x0 ) + y 0 (t)(y − y0 ) + z 0 (t)(z − z0 ) = 0
x − x0 y − y0 z − z0 x0 (t)
y 0 (t)
z 0 (t) = 0.
00
00
x (t) y (t) z 00 (t) x − x0
y − y0
z − z0
0
0
x
y
z0
0 00
00 0
0 00
00 0
0 00
y z − y z z x − z x x y − x00 y 0
Z b
|D| =
= 0.
y(t)|x0 (t)|dt.
a
1Z B 2
|D| =
r (α)dα.
2 A
L=
L=
Z bq
(x0 (t))2 + (y 0 (t))2 dt
Z
a
B
q
(r(α))2 + (r0 (α))2 dα
A
V =π
Z
f =π
K
Pb =
Z
K
ydl = 2π
Z b
y 2 (t)|x0 (t)|dt.
a
Z b
a
q
y(t) (x0 (t))2 + (y 0 (t))2 dt.