8/10/2019 curvas famosas para mate 3 Cisoide de Diocles

1/4

Cisoide de Diocles

Ecuacin cartesiana:

y2=x

3/ (2 a-x)

Ecuacin polar:

r= 2 a(tan ) sin ()

Cardioide

Ecuacin cartesiana:

(x2+ y

2- 2 ax)

2= 4 a

2(x

2+ y

2)

Polar ecuacin:

r= 2 a(1 + cos ( ))

Astroid

Ecuacin cartesiana:

x2/3

+ y2/3

= a3/2

o paramtrica:

x= acos3( t), y= a sin

3( t)

Crculo

Ecuacin cartesiana:

x 2+ y 2= a 2

o paramtrica:

x= acos ( t), y= asen ( t)

la ecuacin polar:r= a

Elipse

Ecuacin cartesiana:

x2/a

2+ y

2/b

2= 1

Polar ecuacin:

x= acos(t), y= bsin(t)

Epicycloid

8/10/2019 curvas famosas para mate 3 Cisoide de Diocles

2/4

Ecuacin cartesiana paramtrica:

x= (a+ b) cos(t) - bcos((a/b+ 1)t),

y= (a+ b) sin(t) - bsin((a/b+ 1)t)

Fermat's Spiral

Polar ecuacion:

r2= a

2

Folium

Cartesian equation:

(x2+ y2)(y2+x(x+ b)) = 4axy2

Polar equation:

r= -bcos+ 4acossin2

Folium of Descartes (hoja de descartes)

Cartesian equation:

x3+ y

3= 3axy

or parametrically:

x= 3at/(1 + t3), y= 3at

2/(1 + t

3)

Hyperbola

Cartesian equation:

x2/a

2- y

2/b

2= 1

or parametrically:

x= asec(t), y= btan(t)

Hiperblica Espiral

Ecuacin polar:

r= a/

8/10/2019 curvas famosas para mate 3 Cisoide de Diocles

3/4

Hypocycloid

Parametric Cartesian equation:

x= (a- b) cos(t) + bcos((a/b- 1)t),

y= (a- b) sin(t) - bsin((a/b- 1)t)

Hipotrocoide

Paramtrico ecuacin cartesiana:

x= ( un- b) cos ( t) + c(cos ( una/ b-1) t),

y= ( un- b) sen ( t) - csin (( un/ b-1 ) t)

Evolvente Realizamos de un Crculo

Paramtrico ecuacin cartesiana:

x= a(cos ( t) + tsen ( t)),

y= a(sin ( t) - tcos ( t))

Lemniscate of Bernoulli

Cartesian equation:

(x2+ y

2)

2= a

2(x

2- y

2)

Polar equation:

r2= a

2cos(2)

Limaon de Pascal

Ecuacin cartesiana:

(x2+ y

2- 2 ax)

2= b

2(x

2+ y

2)

Polar ecuacin:

r= b+ 2 acos ( )

8/10/2019 curvas famosas para mate 3 Cisoide de Diocles

4/4

Spiral of Archimedes

Polar equation:

r= a

Trisectriz de Maclaurin

Ecuacin cartesiana:

y2( a+x) =x

2(3 a-x)

Polar ecuacin:

r= 2 sen (3 ) / sen (2 )

Bruja de Agnesi

Ecuacin cartesiana:

y(x2+ a

2) = a

3

o paramtrica:x= a, y= a/ (1 + t

2)

Tractrix

Paramtrico ecuacin cartesiana:

x= 1 / cosh ( t), y= t- tanh ( t)