The conic sections are curves obtained by making sections, or cuts, at particular angles through a cone. First we will discuss about history of conic sections. Conics are amongst the oldest of the curves, and are the oldest math subject studied systematically and thoroughly. The conics had been discovered by Menaechmus, the tutor to the great Alexander. These conics were perceived in order to solve the three problems (a) trisecting an angle, (b) duplicating the cube, and (c) squaring the circle.
If we cut a cone at different angles, then we will obtain different types of conics. There are four different types of conics that we can obtain. That is circle, where the cone is cut at right angle to its axis, ellipse, where the cone is cut at an oblique angle, parabola, where the cone is cut parallel to the generator and finally hyperbola, where a double cone is cut at an angle steeper than the generator.
Let’s discuss about conic sections formulas and conic sections equations. First is circle, the standard formula of circle is (X^2+y^2=r^2), where centre is (0,0) and radius is r. second is ellipse, the standard formula of a ellipse is (x^2/a^2+y^2/b^2 =1 a = 1/2) length major axis,b = 1/2 length minor axis, third one is parabola, the standard formula of parabola is 4px=y^2, where p=distance from vertex to focus. And the last one is hyperbola, the standard formula of hyperbola is (x^2/a^2-y^2/b^2=1), where a = 1/2 length major axis, b = 1/2 length minor axis. The general equation for all conic section is (Ax^2+Bxy+Cy^2+Dx+Ey+F=0). And by using the quadratic formula
If (B^2-4AC) <0 circle="circle" curve.="curve." curve="curve" ellipse="ellipse" is="is" no="no" or="or" p="p" point="point" the="the" then="then">If (B^2-4AC) =0, then the curve is a parabola or two parallel lines or a single line or no curve.
If (B^2-4AC)>0, then the curve is hyperbola or two intersecting lines.
The procedure of graphing conic sections, in this part first we will focus on graphing circle. If we cut a circular cone with a plane which is perpendicular to the symmetric axis of cone, then a circle is formed. The intersection line is parallel to the plane generating circle of the cone. A circle means from its center all points are at equal distance.
Now graphing of ellipse, in ellipse long axis is major axis and short axis is minor axis. Intersection point of two axis called vertices. The vertices along horizontal and vertical axis form points. This point along with center will provide method to graph ellipse in standard form.
