Crosssection of slices thru a doublenapped (right circular) cone.
Area of a circle = πr^{2}. Circumference = 2πr.
Ellipses centered at (h,k):
Ellipses rotated:
Area of an ellipse = πab.
There is no algebraic formula for the circumference.
But various approximations to within .0015% accuracy exist.
Simple: C≈2π((a+b)/2)
Ramanujan: C≈π[3(a+b)√((3a+b)(a+3b))]
Eccentricity e is a measure of the ovalness/roundness of the ellipse.
0<e<1. Closer to 1: flatter.
Circle is an ellipse in which a=b, the eccentricity e is 0,
and the two foci are the same point, the center of the circle.
Java applet to draw ellipse.
The eccentricity e of every parabola is 1.
Hyperbola centered at (h,k):
Distance from center to focus F is c=√(a^{2}+b^{2})
The eccentricity e=c/a, e>1.
Conic section  e  Equation  

Circle  0  general:  Ax^{2}+Cy^{2}+Dx+Ey+F=0, A=C 
center at origin:  Ax^{2}+Cy^{2}+F=0, A=C  
Ellipse  0<e<1  general:  Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0, B^{2}<4AC 
orthogonal,center at origin:  Ax^{2}+Cy^{2}+F=0, A≠C  
orthogonal,center not at origin:  Ax^{2}+Cy^{2}+Dx+Ey+F=0, A≠C  
Parabola  1  general:  Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0, B^{2}=4AC 
vertical:  Ax^{2}+Dx+Ey+F=0  
horizontal:  Cy^{2}+Dx+Ey+F=0  
Hyperbola  >1  general:  Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0, B^{2}>4AC 
vertical, center at origin:  Ax^{2}+Cy^{2}+F=0  
horizontal, center at origin:  Ax^{2}Cy^{2}+F=0
