Polar and 3D (analysis)

ellipsoid

Elliptic cone

Elliptic paraboloid

Hyperbolic paraboloid (saddle)

Hyperboloid of 1 sheet

Hyperboloid of 2 sheets

Elliptic cylinder

Hyperbolic cylinder

Parabolic cylinder (taco)

Ellipsoid traces

3 ellipses/circles

Elliptic cone traces

2 lines, ellipse

Elliptic paraboloid traces

2 parabolas, ellipse

Hyperbolic paraboloid/saddle traces

2 parabolas opening opposite ways, hyperbola

Hyperboloid of 1 sheet traces

2 hyperbolas, ellipse

Hyperboloid of 2 sheets traces

2 opposite facing parabolas, ellipse

Ellipsoid graph

Elliptic cone graph

Elliptic paraboloid graph

Hyperbolic paraboloid/saddle graph

Hyperboloid of 1 sheet graph

Hyperboloid of 2 sheets graph

Elliptic cylinder graph

Hyperbolic cylinder graph

Parabolic cylinder/taco graph

Limacons equation

r = a+bcostheta

r = a-bcostheta

Rose curves equation

r = acosNtheta

r = asinNtheta

Circles equation

r = acostheta

r = asintheta

Lemniscates equation

r² = a²sin2theta

r² = a²cos2theta

Cardioid graph

Inner loop limacon graph

Dimpled limacon graph

Convex limacon graph

r = acos2theta

r = acos3theta

r = asin2theta

r = asin5theta

r = acostheta

r = asintheta

r² = a²sin2theta

r² = a²cos2theta

r = a

constant r

theta = a

constant theta

r = theta

Cardiod conditions

a = b

Inner loop limacon conditions

b > a

| a/b | < 1

Dimpled limacon conditions

b < a

1 < | a/b | < 2

Convex limacon conditions

2b ≤ a

How to find the first petal location (rose curve)

θ = pi/2n