Purple Math Conic Sections

In the figure shown below cone 1 and cone 2 are connected at the vertex.

Purple math conic sections. Conic sections are the curves which can be derived from taking slices of a double napped cone. Every conic section has certain features including at least one focus and directrix. A double napped cone has two cones connected at the vertex.

Parabolas as conic sections a parabola is the curve formed by the intersection of a plane and a cone when the plane is at the same slant as the side of the cone. The following diagram shows how to derive the equation of circle x h 2 y k 2 r 2 using pythagorean theorem and distance formula. A parabola can also be defined as the set of all points in a plane which are an equal distance away from a given point called the focus of the parabola and a given line called the directrix of the parabola.

An ellipse equation in conics form is always 1 note that in both equations above the h always stayed with the x and the k always stayed with the y the only thing that changed between the two equations was the placement of the a 2 and the b 2 the a 2 always goes with the variable whose axis parallels the wider direction of the ellipse. Ellipse h parabola h hyperbola h definition. Math explained in easy language plus puzzles games quizzes worksheets and a forum.

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. Conic sections math algebra conics circle. A section or slice through a cone.

Defin e conic sections. Hide ads about ads. The b 2 always goes with the variable whose axis.

For any of the below with a center j k instead of 0 0 replace each x term with x j and each y term with y k. A conic section can be graphed on a coordinate plane. Scroll down the page for examples and solutions.