Equations Of Conic Sections Math

A line which a curved function or shape approaches but never touches.

Equations of conic sections math. Parabolas circles ellipses and hyperbolas conic sections received their name because they can each be represented by a cross section of a plane cutting through a cone. X 2 a 2 y 2 b 2 1. A conic section is a curve on a plane that is defined by a 2 nd 2 text nd 2 nd degree polynomial equation in two variables. Conic sections are classified into four groups.

If and it represents pair of straight lines if and it represents a parabola if and it represents an ellipse. Here we will have a look at three different conic sections. X 2 a 2 y 2 b 2 1. And for a hyperbola it is.

Sometimes it is useful to write or identify the equation of a conic section in polar form. Circles and ellipses the equation of a circle with center at a b and radius r units is x a 2 y b 2. X 2 a 2 y 2 a 2 1. We can make an equation that covers all these curves.

Polar equations of conic sections. The types of conic sections are circles ellipses hyperbolas and parabolas. Parabola the parabola is a conic section the intersection of a right circular conical surface and a plane parallel. Equations when placed like this on an x y graph the equation for an ellipse is.

The general equation of the conic section is where this equation can also be analysed to distinguish whether it is an equation of pair of straight lines parabola ellipse or hyperbola. A conic section which does not fit the standard form of equation. Each conic section also has a degenerate form. To do this we need the concept of the focal parameter.

The general equation for any conic section is ax2 bxy cy2 dx ey f 0 where a b c d e and f are constants. As we change the values of some of the constants the shape of the corresponding conic will also change.