Four Conic Sections

There are four basic types.

Four conic sections. The four conic sections conic sections are formed on a plane when that plane slices through the edge of one or both of a pair of right circular cones stacked tip to tip. Here is the major axis and minor axis of an ellipse. Each conic is determined by the angle the plane makes with the axis of the cone.

When x and y are both squared and the coefficients on them are the same including the sign. Depending on the angle between the plane and the cone four different intersection shapes can be formed. Whether the result is a circle ellipse parabola or hyperbola depends only upon the angle at which the plane slices through.

By changing the angle and location of the intersection we can produce different types of conics. When either x or y is squared not both. There is a focus and directrix on each side ie a pair of them.

In an ellipse is 2b 2 a where a and b are one half of the major and minor diameter. Circle ellipse parabola and hyperbola. The ancient greek mathematicians studied conic sections culminating around 200.

Learn about the four conic sections and their equations. The equations y x 2 4 and x 2 y 2 3. Conic sections are a particular type of shape formed by the intersection of a plane and a right circular cone.

The four conic sections. In mathematics a conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane the three types of conic section are the hyperbola the parabola and the ellipse. A conic section is the intersection of a plane and a double right circular cone.