How To Do Conic Sections

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.

How to do conic sections. Given a general form conic equation in the form ax 2 cy 2 dx ey f 0 or after rearranging to put the equation in this form that is after moving all the terms to one side of the equals sign this is the sequence of tests you should keep in mind. When a plane intersects a two napped cone conic sections are formed. The curves are best illustrated with the use of a plane and a two napped cone.

By changing the angle and location of the intersection we can produce different types of conics. When working with circle conic sections we can derive the equation of a circle. The curves can also be defined using a straight line and a point called the directrix and focus.

Conic sections are mathematically defined as the curves formed by the locus of a point which moves a plant such that its distance from a fixed point is always in a constant ratio to its perpendicular distance from the fixed line. A conic section is the intersection of a plane and a cone. The three types of curves sections are ellipse parabola and hyperbola.

A point used to construct and define a conic. The curves ellipse parabola and hyperbola are also obtained practically by cutting the curved surface of a cone in different ways. The graphic below shows how intersections of a two napped cone and a plane form a parabola ellipse circle and a hyperbola.

A straight line which a curve approaches arbitrarily closely as it goes to infinity. There are four basic types. Big small fat skinny vertical horizontal and more.

An extreme point on a conic section. An equation has to have x2 and or y2 to create a conic. A circle has an eccentricity of zero so the eccentricity shows us how un circular the curve is.