Formulas For Conic Sections

Sections of the cone.

Formulas for conic sections. An equation has to have x2 and or y2 to create a conic. The general equation of any conic section is a second order non homogeneous equation in x and y. Apart from focus eccentricity and directrix there are few more parameters defined under conic.

Big small fat skinny vertical horizontal and more. P 0 then left ellipse vertical major axis horizontal major axis equation 2222 22 x h y k 1 ba. If a c and b 0 the equation represents a circle which is a special case of an ellipse.

Conic sections can come in all different shapes and sizes. We can make an equation that covers all these curves. Distance between center and either focus is c with.

The special case of a circle where radius a b. If b2 4ac 0 the equation represents an ellipse. Eccentricity of ellipse e c a a 2 b 2 a latus rectum of ellipse l b 2 a area of ellipse π a b.

Standard forms of equations of conic sections. If a c and b 0 the equation represents a circle which is a. X 2 a 2 y 2 a 2 1.

If neither x nor y is squared then the equation is that of a line. If b2 4ac 0 the equation represents a. And for a hyperbola it is.