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Famous plane curves
Random
Science
or
famous
Quiz
Can you name the plane curves given their graphs?
by
Ignis_Umbrae
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Click the green button to start and enter the correct answers below
If one curve is a special case of another, please give the name specific to the special case. No equation is provided for #8, because every one is extremely complicated.
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Number
Curve
Defining equation (e.g.)
1
(x,y) = a(cos
^{3}
(t), sin
^{3}
(t))
2
(x,y) = (acos(t), bsin(t))
3
(x,y) = 2aπ
^{1}
(t cot(t), t)
4
(x,y) = a(3cos(t)  cos(3t), 3sin(t)  sin(3t))
5
(x,y) = a(t  sin(t), 1  cos(t))
6
(x,y) = (t, sin(t))
7
(x,y) = 2a(t, 1/(t
^{2}
+1))
8

9
(x,y) = (a sec(t), b tan(t))
10
x
^{3}
+ y
^{3}
= 3xy
Number
Curve
Defining equation (e.g.)
11
y
^{2}
(a
^{2}
 x
^{2}
) = (x
^{2}
+ 2ay  a
^{2}
)
^{2}
12
(x,y) = a(t  tanh(t), sech(t))
13
(x,y) = a(cos(t), sin(t))
14
r = a √(cos(2θ))
15
y
^{4}
a
^{2}
y
^{2}
=x
^{2}
b
^{4}
x
^{2}
16
(x,y) = a(C(t), S(t))
17
3ax
^{2}
 ay
^{2}
+ x
^{3}
+ xy
^{2}
=0
18
r = a(1  cos(θ))
19
ax + by + c = 0
20
r = a sin(θ)/θ
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