Conic Sections Research Paper

Conic sections are used all over the world. Conic sections are used in things such as bridges, roller coasters, stadiums, and other objects. A conic section is the intersection of a plane with a cone. The changes in the angle of the intersection produce a circle, ellipse, parabola, and hyperbola. All the types of conic sections can be identified using the general form equation. The general form equation is x2+Bxy+Cy2+Dx+Ey+F=0. Using the general form equation can help identify each type of conic section. If B2-4AC < 0, if there is 2 squared terms, and if the coefficients have the same sign, but different numbers then it is an ellipse. If B2-4AC > 0, if there is 2 squared terms, and one has a negative coefficient then it is a hyperbola. If there is 2 squared terms, and both coefficients are the same then it is a circle. If B2-4AC = 0, and there is only one squared term it is a parabola.

To make an equation from a graph you take the center point and plug it in for h and k, and then you count how far one of the sides is from the center and plug that into the radius. In order to identify if it is a equation for a circle the x and y have to be squared and have the same coefficients. A parabola is easy because either x or y are squared, so only one. To identify an ellipse the equation has to have x and y squared that are positive but the coefficients are different numbers. A hyperbola equation has x and y squared and a coefficiet is negative and he other is posive Hyperbola. When x and y are both squared, and exactly one of the coefficients is negative and exactly one of the coefficients is