A Book of Curves

astroid asymptotes axes base-circle called cardioid Cartesian equation catenary caustic chord circle at Q circle of radius circle rolls circle whose centre circle with respect circumference cissoid conchoid congruent constant coordinates cusp-point cusps cutting the circle cycloid deltoid diameter directrix Draw a circle Draw a Lemniscate drawn ellipse envelope epicycloid epitrochoid equiangular spiral evolute fixed circle fixed line fixed point focus geometrical glissette Hence Hint for proof hyperbola with respect hypocycloid initial line instantaneous centre intersection inverse involute lemniscate of Bernoulli length limaçon locus mark points meet mid-point moves negative pedal nephroid normal original curve paper parabola parallel Parametric equations pedal curve pedal equation perpendicular polar equation pole position produced properties prove radii radius 2a rectangular hyperbola right angles right strophoid rolling circle roulette set square sinusoidal spiral subtends Suitable Dimensions tangent tractrix triangle trisectrix vertex