Level 538 Level 540
Level 539

Conic Sections in Polar Coordinates


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Parabola
r = 3/(1+sinθ)
r=12/(2+4cosθ)
Hyperbola
r=6/(3+2cosθ)
Ellipse
r=8/(2-4cosθ)
Hyperbola
r=8/(4+4sinθ)
Parabola
r=9/(3-9cosθ)
Hyperbola
r=4/(2-cosθ)
Ellipse
r = a
Polar Curves: Circle - centered at pole
r = a cos Θ
Polar Curves: Circle - shifted along the x-axis
r = a sin Θ
Polar Curves: Circle - shifted along the y-axis
Line
A straight path that goes without end in two directions.
line (vertical)
r cos Θ = a
line (horizontal)
r sin Θ = a
cardioid (horizontal)
r = a ± a cos Θ
cardioid (vertical)
r = a ± a sin Θ
limacon w/ loop (horizontal)
r = a ± b cos Θ (a < b)
limacon w/ loop (vertical)
r = a ± b sin Θ (a < b)
limacon w/o loop (horizontal)
r = a ± b cos Θ (a > b)
limacon w/o loop (vertical)
r = a ± b sin Θ (a > b)
rose w/ n petals
r = a cos nΘ (n is odd)
rose w/ 2n petals
r = a cos nΘ (n is even)
Lemniscate
r² = a cos 2Θ
lemniscate at an angle
r² = a sin 2Θ
Archimede's spiral
r = aΘ