{"id":10786,"date":"2016-05-25T16:01:54","date_gmt":"2016-05-25T08:01:54","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=10786"},"modified":"2016-05-25T16:03:35","modified_gmt":"2016-05-25T08:03:35","slug":"conic-sections-interactive-applet","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/conic-sections-interactive-applet-10786","title":{"rendered":"Conic sections interactive applet"},"content":{"rendered":"

I recently updated the conic sections interactive applet<\/a>, part of the Plane Analytic Geometry section. <\/p>\n

The applet now uses a different back-end meaning that it's now mobile-friendly and somewhat more convincing. <\/p>\n

Using the applet you can explore the conic shapes that occur when you slice a double cone by a plane at various angles and positions.<\/p>\n

You will get either a circle, ellipse, parabola<\/strong> or hyperbola<\/strong>. Such curves are called conic sections<\/strong>, since they are the result of slicing a cone with a plane.<\/p>\n

Example output<\/h2>\n

When the plane's angle is less than the cone's side angle, we get an ellipse, as follows: <\/p>\n

\n

\"ellipse
\n Conic section - Ellipse <\/p>\n<\/p>\n<\/div>\n

If the angle of the plane is greater than the angle of the sides of the cone, the result is a hyperbola:<\/p>\n

\"hyperbola
\n Conic section - Hyperbola<\/div>\n

At various extremeties, you get a degenerate conic<\/strong>, which is either a:<\/p>\n