4. Cardioid
Cartesian Equation of Cardioid is
(x2 + y2 ⎼ 2ax)2 = 4a2(x2 + y2)
Polar Equation of Cardioid is
r = 2a(1 + cosθ)
Parametric Equations are
- x(t) = a[2 cos t ⎼ cos(2t)]
- y(t) = a[2 sin t ⎼ sin(2t)]
Notable Facts:
- (a) There are exactly three parallel tangents at any given point on the cardioid.
- (b) The tangents at the ends of any chord through the cusp point are at right angles.
- (c) Trace a point on the circle rolling around another circle of equal radius.
Parabola.
Circle.
Ellipse.
Hyperbola.
1. Astroid
Bicorn
Cardioid
Cartesian Oval
Cassinian Ovals
Catenary
Cayley’s Sextic
Circle
Cissoid of Diocles
Cochleoid
Conchoid
Conchoid of de Sluze
Cycloid
Devil’s Curve
Double Folium
Durer’s Shell Curves
Figure Eight Curve
Ellipse
Epicycloid
Epitrochoid
Equiangular Spiral
Fermat’s Spiral
Folium
Folium of Descartes
Freeth’s Nephroid
Frequency Curve
Hyperbola
Hyperbolic Spiral
Hypocycloid
Hypotrochoid
Involute of a Circle
Kampyle of Eudoxus
Kappa Curve
Lame Curves
Lemniscate of Bernoulli
Limacon of Pascal
Lissajous Curves
Lituus
Neile’s Semi-cubical Parabola
Nephroid
Newton’s Diverging Parabolas
Parabola
Pearls of Sluze
Pear-shaped Quartic
Plateau Curves
Pursuit Curve
Quadratrix of Hippias
Rhodonea Curves
Right Strophoid
Serpentine
Sinusoidal Spirals
Spiral of Archimedes
Spiric Sections
Straight Line
Talbot’s Curve
Tractrix
Tricuspoid
Trident of Newton
Trifolium
Trisectrix of Maclaurin
Tschirnhaus’s Cubic
Watt’s Curve Witch of Agnesi