## Conic Section

 A fascinating fact about the motions of all heavenly bodies (planets, comets, etc.) is that they all move in conic sections. Conic sections are the ellipse, parabola, hyperbola, and the circle . In fact all objects under the influence of gravity moves in conic sections.    Conic sections can be written in mathematics and they are as follows : I. Circles. A circle is the set of points in a plane whose distance from a given fixed point in the plane is constant. The fixed point is the center of the circle ; the constant distant is the radius . The equation of a circle of radius centered at the point (h,k) is : (x-h)2 + (y-k)2 = a2 (a is the radius of the circle.) II. Parabolas. A set that consists of all the points in a plane equidistant from a given fixed point and a given fixed line in the plane is a parabola . The fixed point is the focus of the parabola. The fixed line is the directrix . It's standard form is : y = x2 / 4p (p is the parabola's focal length.) III. Ellipses. An ellipse is the set of points in a plane whose distances from two fixed points in a plane have a constant sum. The two fixed points are the foci of the ellipse. It's standard form is : x2 / a2 + y2 / b2 = 1 (a>0 , b>0) (a is the semimajor axis and b is the simiminor axis of the ellipse.) IV. Hyperbolas. A hyperbola is the set of points in a plane whose distances from two fixed points in the plane have a constant difference. The two fixed points are the foci of the hyperbola. It's standard form is : x2 / a2 - y2 / b2 = 1 (a>0 , b>0 , k2 = a2 + b2)