Conic Sections
Conics
plot a conic section and identify its type
x^2 - 2 y^2 = 1
2x^2 - 3xy + 4y^2 + 6x - 3y - 4 = 0
Circles
compute properties of a circle
circle of radius 2 with center (0,-2)
circle with area 30cm^2
find a circle passing through three points
circle through (0,0), (1,0), (0,1)
compute the circumference of a circle
circumference of a circle with radius 3 miles
Ellipses
compute properties of an ellipse
ellipse with semiaxes 2,5 centered at (3,0)
ellipse with eccentricity 1/2
specify an ellipse by its equation
ellipse with equation (x-2)^2/25 + (y+1)^2/10 = 1
compute the eccentricity of an ellipse
eccentricity of an ellipse with semiaxes 12,1
compute the focal parameter of an ellipse
focal parameter of an ellipse with semiaxes 4,3
Parabolas
compute properties of a parabola
parabola with focus (3,4) and vertex (-4,5)
parabola (y-2)^2=4x
compute the directrix of a parabola
directrix of parabola x^2+3y=16
Hyperbolas
compute properties of a hyperbola
hyperbola with center (100, 200) and focus (110, 180)
hyperbola semimajor axis 10, focal parameter 2
locate the foci of a hyperbola