Conic Section Equations

The equation for a parabola is.

Conic section equations. And for a hyperbola it is. X 2 a 2 y 2 a 2 1. Conic sections and standard forms of equations a conic section is the intersection of a plane and a double right circular cone.

The appearance of each conic section has trends based on the values of the constants in the equation. The ancient greek mathematicians studied conic sections culminating around 200. Frac 2b 2 a conic section formulas examples.

The equations of conic sections are very important because they tell you not only which conic section you should be graphing but also what the graph should look like. Find an equation of the circle with centre at 0 0 and radius r. Conic sections formulas parabola vertical axis horizontal axis equation x h 2 4p y k y k 2 4p x h axis of symmetry x h y k vertex h k h k focus h k p h p k directrix y k p x h p direction of opening p 0 then up.

Conic sections are the curves which can be derived from taking slices of a double napped cone. These take the form of points and lines. We can make an equation that covers all these curves.

The types of conic sections are circles ellipses hyperbolas and parabolas. Conic section formulas for latus rectum in hyperbola. A double napped cone in regular english is two cones nose to nose with the one cone balanced perfectly on the other section here is used in a sense similar to that in medicine or science where a sample from a.

Therefore the equation of the circle is x 2 y 2 r 2. A line which a curved function or shape approaches but never touches. P 0 then down p 0 then rignt.