Bard Math 212 - Quadric Surface

558 days ago by ethan

Ellipsoid

\displaystyle \frac {x^2}{a^2} + \frac {y^2}{b^2} + \frac {z^2}{c^2} = 1
x, y, z = var('x,y,z') implicit_plot3d(x^2/4^2 + y^2/3^2 + z^2/2^2==1, (x,-8, 8), (y,-6,6), (z,-4,4), aspect_ratio=1) 
       

Elliptic Paraboloid

\displaystyle \frac zc = \frac {x^2}{a^2} + \frac {y^2}{b^2}
x, y, z = var('x,y,z') implicit_plot3d(x^2/4^2 + y^2/3^2 - z/2==0, (x,-8, 8), (y,-6,6), (z,-4,4), aspect_ratio=1) 
       

Hyperbolic Paraboloid

\displaystyle \frac zc = \frac {x^2}{a^2} - \frac {y^2}{b^2}
x, y, z = var('x,y,z') implicit_plot3d(x^2/4^2 - y^2/3^2 - z/2==0, (x,-8, 8), (y,-6,6), (z,-4,4), aspect_ratio=1) 
       

Cone

\displaystyle \frac {z^2}{c^2} = \frac {x^2}{a^2} + \frac {y^2}{b^2}
x, y, z = var('x,y,z') implicit_plot3d(x^2/4^2 + y^2/3^2 - z^2/2^2==0, (x,-8, 8), (y,-6,6), (z,-4,4), aspect_ratio=1) 
       

Hyperboloid of One Sheet

\displaystyle \frac {x^2}{a^2} + \frac {y^2}{b^2} - \frac {z^2}{c^2} = 1
x, y, z = var('x,y,z') implicit_plot3d(x^2/4^2 + y^2/3^2 - z^2/2^2==1, (x,-8, 8), (y,-6,6), (z,-4,4), aspect_ratio=1) 
       

Hyperboloid of Two Sheets

\displaystyle - \frac {x^2}{a^2} - \frac {y^2}{b^2} + \frac {z^2}{c^2} = 1
x, y, z = var('x,y,z') implicit_plot3d(- x^2/4^2 - y^2/3^2 + z^2/2^2==1, (x,-8, 8), (y,-6,6), (z,-4,4), aspect_ratio=1)